互补问题最优化算法研究及其应用
|
摘要
最优化理论与算法是一门广泛应用的学科,它主要讨论决策问题的最佳选择之特性,并构造寻求最佳的计算方法,以及研究这些计算方法的理论性质和实际计算效果。数学规划是最优化理论的一个重要分支,和其它数学分支相比,它是一门非常年轻但又十分活跃的应用数学分支。而互补问题又是另外一类相当广泛的数学模型。事实上,许多实际问题的数学模型其实就是一个特殊的互补问题,并且经典的线性规划问题与非线性问题都可以转化为互补问题来进行求解计算。
1947年,Danzig提出了线性规划的概念及其著名的单纯型算法,该算法在实际计算过程中具有良好的计算性能,但从理论上来讲其复杂性并不理想,主要原因是随着问题规模的扩大,算法迭代次数迅速增长,这给实际计算带来很大的麻烦。受计算复杂性理论的影响,很多学者曾在很长一段时间内,希望通过证明单纯形法具有多项式时间算法。但是,Klee和Minty在1972年通过举反例,证明了单纯形算法法它并不是一个多项式算法,这样线性规划问题是否存在多项式算法就成为众多学者迫切想知道的问题。接下来,在1979年,Khachiyan针对线性规划问题是否为多项式算法的这一困惑,提出了著名的“椭球算法”,该算法是线性规划的第一个多项式算法,但是此算法的理论上的优势并不能在实际计算性能上超越单纯形算法法,这就引起了众多学者试图再去寻找另外一种新的具有较好实际计算性能的线性规划的多项式算法。直到1984年,Karmarkar的“投影尺度算法”使得线性规划算法出现了真正的突破,这种新算法不仅在理论上优越于单纯形算法,而且也显示出对求解大规模实际问题的巨大潜力。Karmarkar算法再一次真正不同于单纯形算法(单纯性算法是从可行域的一个顶点迭代到另外一个顶点,直到达到问题的最优解),而Karmarkar算法它是从可行域的内部沿着某个方向逼近问题的最优解,所以有时候也称为“内点算法”。
经过众多学者对Karmarkar内点算法的深入探讨与研究,现在已经发展成最具有代表性的有三类：势函数下降投影变换方法(即Karmarkar内点算法)、仿射均衡变换方法和原始-对偶跟踪中心轨迹方法。虽然这三大类内点算法具有很强的计算效果,但是现有可行内点算法也并非完美无缺,其中最突出的问题是,由其计算复杂性分析所得出的多项式时间界限不能作为衡量一个算法好坏的唯一依据,其原因如下：
其一,小步长(窄邻域)原始-对偶内点算法的多项式复杂性为O((?)nlog(n/ε)),远远低于大步长(宽邻域)原始-对偶内点算法的复杂性O(n log(n/ε)).但是在实际的计算效果上,前者计算效果比后者差很多(主要原因是小步长算法较大步长算法极大的限制了步长的选取)。针对这种不一致现象,在90年代,Ye和Huang提出了一种高阶(r阶)预估校正原始-对偶大步长(宽邻域)内点算法,将算法的迭代复杂性降到O(n(r+1)/(2r)L),其中r∈[1,n)。可以看出,当r=n时,该算法的迭代复杂性近似变为O(√nL)。而其他基于高阶内点算法来降低大步长(宽邻域)原始-对偶内点算法的工作也有一些。比如,Peng等人通过定义自正则(Self-Regular)邻近度量,用这种新的分析工具将大步长(宽邻域)内点算法的多项式时间复杂性降低到O(nq+1/2qlog(n/ε))其中q>1。2006年,Pan等人通过分析发现,上述自正则邻近度量方法在证明上面的结论时所使用的牛顿方向,是通过对“中心方程”用一个等价的幂等变换得到。虽然这种幂函数变换从代数意义上讲等价的,但是到达最优解的速度却不一样,而且也容易理解。因此,基于适当的代数等价变换,也可以达到降低原始-对偶内点算法的计算复杂性的效果。
其二,就是可行内点算法在初始迭代点选取上太过于苛刻,既要满足严格等式约束又要满足非负约束条件,并且在实际问题中这种初始点的选取很难获得,而不可行内点算法却放松了这一条件,只要在迭代开始时满足非负条件,而不再需要满足等式约束。这一放松大大降低了初始可行点在选取上的困难性。因此,不可行内点算法在处理实际问题中被广泛应用。
本文主要分为理论和应用两大部分。第一部分(第二章到第五章),理论部分主要利用优化算法解决一些理论上存在的问题,比如大步长与小步长在迭代与计算复杂性上的矛盾以及初始可行点在选取上的困难等；第二部分(第六、七章)是利用优化算法解决一些实际问题,如利用之前的内点算法中的路径跟踪算法和仿射尺度算法解决双矩阵对策问题以及利用优化问题和演化博弈算法解决农村合作组织中的经济问题,通过编程简单的模拟算法的迭代过程以及最后的稳定状态。
在理论部分,首先在前人的研究基础上,将P矩阵线性互补问题高阶内点算法推广到更一般的P.(k)阵高阶线性互补问题中去,并基于不同的邻域(大步长和小步长)讨论了算法的复杂性。其次,基于代数等价变换的思想以及KMM算法的框架,对P0阵线性互补问题提出了新的原始-对偶不可行内点算法。该算法的创新点首先是基于KMM算法的框架,该算法在处理不可行内点算法结构上很简单,其次就是利用一个特殊的代数等价代换,因此在复杂性上较之前的算法有了很大改进,主要体现在代数等价变换上,虽然从代数的角度上是等价的,但是达到最优解的速度却不相同,可以在后面的数值试验中体现出来。最后,在前人的研究基础上,将线性规划问题推广到更一般的互补问题中去,分别讨论了基于核函数求解线性互补问题和非线性互补问题的不可行内点算法并证明了其计算具有多项式复杂性,在讨论非线性互补问题时,在前人研究的基础上,构造了一个新的核函数,利用该函数来衡量算法是否达到最优解,最后证明算法经过次迭代达到问题的最优解。
第二部分为应用部分,由于互补问题是一类非常重要的优化问题,它广泛应用在经济分析、交通平衡策略等社会经济模型中。因此,对互补问题的研究具有十分重要的现实意义。所以,本文第六章以博弈论理论为基础,探讨了线性互补问题在经济学中的双矩阵博弈中的应用,并提炼出了两个典型双矩阵博弈实例(囚徒困境博弈和监察博弈),借鉴线性互补问题中的势函数下降法和中心路径跟踪算法有效的解决了上述实例。
其次是利用演化博弈理论和最优化算法探求农村合作组织的合作机制,建立了异质农民群体(具有组织管理才能与影响力的阶层与普通农民阶层)在农村合作组织运行的演化博弈模型,局中人根据前一轮合作的结果,通过模仿或学习调整下一轮是否合作的博弈对策,逐步寻求演化稳定均衡解。为了求出演化稳定均衡解提出了一种新的演化博弈算法。该算法的基本思想是将最优化问题的搜索空间映射到博弈论中的策略组合空间中去,目标函数f映射到博弈论的效用函数,通过不完全理性博弈主体的达到局部稳定均衡状态,根据据局部均衡结果博弈主体调整各自对策,进行下一轮博弈,搜寻到更优的均衡,最终达到演化稳定均衡解,从而求解出实际问题的进化稳定状态。
Optimization theory and algorithm is a widely used discipline, it is mainly to discuss the best method of the decision-making problem, to seek the optimum calculation method, theoretical properties of these calculation methods and practical calculation performance. Mathematical programming is an important branch of optimization theory, compared with other branches of mathematics, it is a very young and very active branch of applied mathematics. The complementarity problem is a kind of mathematical model of considerable. In fact, the mathematical model for many practical problems is a special complementarity problem, linear programming problems and nonlinear classic problem can be transformed into complementary problem to solve calculation.
Since1947, Danzig proposed the concept of linear programming and the famous simplex algorithm, the algorithm has a good performance in the actual process of calculation, but in theory of complexity,it is not ideal. Affected by the computational complexity theory, scholars have had a lot of time to hope that simplex method has a polynomial time algorithm. However, in1972,Klee and Minty used the example, proved the simplex algorithm method, it is not a polynomial algorithm, this is a very significant issue:whether the linear programming problems have polynomial algorithm? In1978, Khachiyan gave the linear programming problem a new method,the ellipsoid algorithm, this algorithm is a linear programming algorithm, but on theoretical, advantages are not in the actual computational performance beyond simple simplex method, which had caused many scholars try to find the linear programming with polynomial algorithm better practical performance calculation another. Until1984, the "Karmarkar" made the projective scaling algorithm for linear programming and had a true breakthrough, this new algorithm not only in theory was superior to the simplex algorithm, but also showed great potential in solving large-scale problems. The Karmarkar algorithm was again really different from simplex algorithm (a vertex of feasible region from iteration to another vertex), its approximation from inside the feasible region one of the optimal solution, it is known as the "interior point algorithm".
According to in-depth study of the Karmarkar algorithm by a lot of scholars, had been the development of the most representative of three categories:projection transformation method decreased potential function (Karmarkar algorithm), trajectory method for balancing transform and affine tracking center. But the existing feasible interior point algorithm is also not be the pink of perfection, the most prominent problem is polynomial time bounds, complexity analysis obtained but not as the only measure of an algorithm by calculation.
First, small step (narrow neighborhood) primal-dual interior point algorithm for polynomial complexity is O(Vn log((?)nlog(n/ε)), far below the size (wide neighborhood) complexity of primal-dual interior point algorithm-O(n log(n/ε)), But in the calculation of actual effects, the former is than the latter with a lot of calculation results. In view of this inconsistent phenomenon, in the90's, Ye and Huang proposed a higher order (r order) predictor-corrector primal-dual size (wide neighborhood) interior point algorithm, the iteration complexity is reduced to O(nr+1/2r log(n/ε)),(where r∈[1,n]),among them. We can find that, iterative approximation to the time complexity of the algorithm, And the other based on high order interior point algorithm to reduce the size (wide neighborhood) primal-dual interior point algorithm work had another. For example, Peng et al. By defining the self-regular proximity measure (Self-Regular), the large step with this new analytical tool (wide-neighborhood interior-point algorithm) polynomial time complexity was reduced to O(nq+1/2q log(n/ε)),(where q>1), among them. In2006, Pan et al found by analysis, Newton direction of the self-regular proximity measure method used in the proof of the above conclusions, was through the "central equation" with an equivalent was idempotent transformation. Although the power function transformation from algebraic sense equivalent, but the speed to the optimal solution was not the same. Therefore, algebraic transformation based on proper, also can be reduced the computational complexity of primal-dual interior point algorithm.
Second, it is the feasible interior point algorithm in the initial iteration point selection is too demanding, not only to meet the strict equality constraints and nonnegative condition, and selecting the initial points in practical problems are hard to get, but infeasible interior point algorithm for relaxing the conditions, as long as it meets the nonnegative condition in the iteration begins, without the need to satisfy the equality constraints. This greatly reduces the difficulty in selecting the initial feasible point. Therefore, infeasible interior point algorithm in dealing with practical problems are widely used.
This paper is divided into two parts, theory and application. The first part, solve some theory problems of optimization algorithms mainly use the theory part; the second part, the application part is mainly used to solve some practical problems of optimization algorithm.
In the theory part, we firstly discussed the different neighborhood (based on large step size and small step size) for solving non-monotone linear complementary problem of higher order interior point algorithm. Secondly, ideas and framework of algebraically equivalent transformation based on KMM algorithm for linear complementarity problems, put forward a new primal-dual infeasible interior point algorithm, the global convergence of the algorithm. And the effectiveness of the algorithm is tested by numerical experiments. Finally, discussed based on kernel function to solve the infeasible interior point algorithm and prove its computational complexity and similar kernel function for solving nonlinear complementarity problem based on kernel function.
The second part is the application part, because that the complementarity problem is an important optimization problem, which is widely used in economic analysis, traffic equilibrium strategies of social economic model. So it is the very vital significance to research the study of complementarity problems. Therefore, the department based on economics theory as a foundation, discusses the application of linear complementary double matrix game problem in economics, and a collection of two typical double matrix game example (prisoner's dilemma game and inspect the game), potential function usd by linear complementarity problem and the descent method and path tracking algorithm the effective solution to test the above example.
Second is the use of cooperative mechanism of evolutionary game theory and optimization algorithm for rural cooperative organization, established heterogeneous groups of farmers (with organization and management ability and influence of the class and ordinary peasant class) in the evolution game model of operation of rural cooperative organization, in the previous round of cooperation according to the results, whether the cooperation game under the adjustment a round, gradually seek evolutionary stable equilibrium solution. In order to find the evolution stable equilibrium solution presents a new evolutionary algorithm. The basic idea of the algorithm is the combination of strategies space search space optimization problem is mapped to game theory in the objective function, the utility function is mapped to the game theory, the irrational game subject to local stable equilibrium state, according to local equilibrium Kobo subject to adjust their own strategy, the next round of the game, to search for better reach equilibrium, evolutionarily stable equilibrium solution, thus solving the evolutionary stable state of the actual problem.
1947年,Danzig提出了线性规划的概念及其著名的单纯型算法,该算法在实际计算过程中具有良好的计算性能,但从理论上来讲其复杂性并不理想,主要原因是随着问题规模的扩大,算法迭代次数迅速增长,这给实际计算带来很大的麻烦。受计算复杂性理论的影响,很多学者曾在很长一段时间内,希望通过证明单纯形法具有多项式时间算法。但是,Klee和Minty在1972年通过举反例,证明了单纯形算法法它并不是一个多项式算法,这样线性规划问题是否存在多项式算法就成为众多学者迫切想知道的问题。接下来,在1979年,Khachiyan针对线性规划问题是否为多项式算法的这一困惑,提出了著名的“椭球算法”,该算法是线性规划的第一个多项式算法,但是此算法的理论上的优势并不能在实际计算性能上超越单纯形算法法,这就引起了众多学者试图再去寻找另外一种新的具有较好实际计算性能的线性规划的多项式算法。直到1984年,Karmarkar的“投影尺度算法”使得线性规划算法出现了真正的突破,这种新算法不仅在理论上优越于单纯形算法,而且也显示出对求解大规模实际问题的巨大潜力。Karmarkar算法再一次真正不同于单纯形算法(单纯性算法是从可行域的一个顶点迭代到另外一个顶点,直到达到问题的最优解),而Karmarkar算法它是从可行域的内部沿着某个方向逼近问题的最优解,所以有时候也称为“内点算法”。
经过众多学者对Karmarkar内点算法的深入探讨与研究,现在已经发展成最具有代表性的有三类：势函数下降投影变换方法(即Karmarkar内点算法)、仿射均衡变换方法和原始-对偶跟踪中心轨迹方法。虽然这三大类内点算法具有很强的计算效果,但是现有可行内点算法也并非完美无缺,其中最突出的问题是,由其计算复杂性分析所得出的多项式时间界限不能作为衡量一个算法好坏的唯一依据,其原因如下：
其一,小步长(窄邻域)原始-对偶内点算法的多项式复杂性为O((?)nlog(n/ε)),远远低于大步长(宽邻域)原始-对偶内点算法的复杂性O(n log(n/ε)).但是在实际的计算效果上,前者计算效果比后者差很多(主要原因是小步长算法较大步长算法极大的限制了步长的选取)。针对这种不一致现象,在90年代,Ye和Huang提出了一种高阶(r阶)预估校正原始-对偶大步长(宽邻域)内点算法,将算法的迭代复杂性降到O(n(r+1)/(2r)L),其中r∈[1,n)。可以看出,当r=n时,该算法的迭代复杂性近似变为O(√nL)。而其他基于高阶内点算法来降低大步长(宽邻域)原始-对偶内点算法的工作也有一些。比如,Peng等人通过定义自正则(Self-Regular)邻近度量,用这种新的分析工具将大步长(宽邻域)内点算法的多项式时间复杂性降低到O(nq+1/2qlog(n/ε))其中q>1。2006年,Pan等人通过分析发现,上述自正则邻近度量方法在证明上面的结论时所使用的牛顿方向,是通过对“中心方程”用一个等价的幂等变换得到。虽然这种幂函数变换从代数意义上讲等价的,但是到达最优解的速度却不一样,而且也容易理解。因此,基于适当的代数等价变换,也可以达到降低原始-对偶内点算法的计算复杂性的效果。
其二,就是可行内点算法在初始迭代点选取上太过于苛刻,既要满足严格等式约束又要满足非负约束条件,并且在实际问题中这种初始点的选取很难获得,而不可行内点算法却放松了这一条件,只要在迭代开始时满足非负条件,而不再需要满足等式约束。这一放松大大降低了初始可行点在选取上的困难性。因此,不可行内点算法在处理实际问题中被广泛应用。
本文主要分为理论和应用两大部分。第一部分(第二章到第五章),理论部分主要利用优化算法解决一些理论上存在的问题,比如大步长与小步长在迭代与计算复杂性上的矛盾以及初始可行点在选取上的困难等；第二部分(第六、七章)是利用优化算法解决一些实际问题,如利用之前的内点算法中的路径跟踪算法和仿射尺度算法解决双矩阵对策问题以及利用优化问题和演化博弈算法解决农村合作组织中的经济问题,通过编程简单的模拟算法的迭代过程以及最后的稳定状态。
在理论部分,首先在前人的研究基础上,将P矩阵线性互补问题高阶内点算法推广到更一般的P.(k)阵高阶线性互补问题中去,并基于不同的邻域(大步长和小步长)讨论了算法的复杂性。其次,基于代数等价变换的思想以及KMM算法的框架,对P0阵线性互补问题提出了新的原始-对偶不可行内点算法。该算法的创新点首先是基于KMM算法的框架,该算法在处理不可行内点算法结构上很简单,其次就是利用一个特殊的代数等价代换,因此在复杂性上较之前的算法有了很大改进,主要体现在代数等价变换上,虽然从代数的角度上是等价的,但是达到最优解的速度却不相同,可以在后面的数值试验中体现出来。最后,在前人的研究基础上,将线性规划问题推广到更一般的互补问题中去,分别讨论了基于核函数求解线性互补问题和非线性互补问题的不可行内点算法并证明了其计算具有多项式复杂性,在讨论非线性互补问题时,在前人研究的基础上,构造了一个新的核函数,利用该函数来衡量算法是否达到最优解,最后证明算法经过次迭代达到问题的最优解。
第二部分为应用部分,由于互补问题是一类非常重要的优化问题,它广泛应用在经济分析、交通平衡策略等社会经济模型中。因此,对互补问题的研究具有十分重要的现实意义。所以,本文第六章以博弈论理论为基础,探讨了线性互补问题在经济学中的双矩阵博弈中的应用,并提炼出了两个典型双矩阵博弈实例(囚徒困境博弈和监察博弈),借鉴线性互补问题中的势函数下降法和中心路径跟踪算法有效的解决了上述实例。
其次是利用演化博弈理论和最优化算法探求农村合作组织的合作机制,建立了异质农民群体(具有组织管理才能与影响力的阶层与普通农民阶层)在农村合作组织运行的演化博弈模型,局中人根据前一轮合作的结果,通过模仿或学习调整下一轮是否合作的博弈对策,逐步寻求演化稳定均衡解。为了求出演化稳定均衡解提出了一种新的演化博弈算法。该算法的基本思想是将最优化问题的搜索空间映射到博弈论中的策略组合空间中去,目标函数f映射到博弈论的效用函数,通过不完全理性博弈主体的达到局部稳定均衡状态,根据据局部均衡结果博弈主体调整各自对策,进行下一轮博弈,搜寻到更优的均衡,最终达到演化稳定均衡解,从而求解出实际问题的进化稳定状态。
Optimization theory and algorithm is a widely used discipline, it is mainly to discuss the best method of the decision-making problem, to seek the optimum calculation method, theoretical properties of these calculation methods and practical calculation performance. Mathematical programming is an important branch of optimization theory, compared with other branches of mathematics, it is a very young and very active branch of applied mathematics. The complementarity problem is a kind of mathematical model of considerable. In fact, the mathematical model for many practical problems is a special complementarity problem, linear programming problems and nonlinear classic problem can be transformed into complementary problem to solve calculation.
Since1947, Danzig proposed the concept of linear programming and the famous simplex algorithm, the algorithm has a good performance in the actual process of calculation, but in theory of complexity,it is not ideal. Affected by the computational complexity theory, scholars have had a lot of time to hope that simplex method has a polynomial time algorithm. However, in1972,Klee and Minty used the example, proved the simplex algorithm method, it is not a polynomial algorithm, this is a very significant issue:whether the linear programming problems have polynomial algorithm? In1978, Khachiyan gave the linear programming problem a new method,the ellipsoid algorithm, this algorithm is a linear programming algorithm, but on theoretical, advantages are not in the actual computational performance beyond simple simplex method, which had caused many scholars try to find the linear programming with polynomial algorithm better practical performance calculation another. Until1984, the "Karmarkar" made the projective scaling algorithm for linear programming and had a true breakthrough, this new algorithm not only in theory was superior to the simplex algorithm, but also showed great potential in solving large-scale problems. The Karmarkar algorithm was again really different from simplex algorithm (a vertex of feasible region from iteration to another vertex), its approximation from inside the feasible region one of the optimal solution, it is known as the "interior point algorithm".
According to in-depth study of the Karmarkar algorithm by a lot of scholars, had been the development of the most representative of three categories:projection transformation method decreased potential function (Karmarkar algorithm), trajectory method for balancing transform and affine tracking center. But the existing feasible interior point algorithm is also not be the pink of perfection, the most prominent problem is polynomial time bounds, complexity analysis obtained but not as the only measure of an algorithm by calculation.
First, small step (narrow neighborhood) primal-dual interior point algorithm for polynomial complexity is O(Vn log((?)nlog(n/ε)), far below the size (wide neighborhood) complexity of primal-dual interior point algorithm-O(n log(n/ε)), But in the calculation of actual effects, the former is than the latter with a lot of calculation results. In view of this inconsistent phenomenon, in the90's, Ye and Huang proposed a higher order (r order) predictor-corrector primal-dual size (wide neighborhood) interior point algorithm, the iteration complexity is reduced to O(nr+1/2r log(n/ε)),(where r∈[1,n]),among them. We can find that, iterative approximation to the time complexity of the algorithm, And the other based on high order interior point algorithm to reduce the size (wide neighborhood) primal-dual interior point algorithm work had another. For example, Peng et al. By defining the self-regular proximity measure (Self-Regular), the large step with this new analytical tool (wide-neighborhood interior-point algorithm) polynomial time complexity was reduced to O(nq+1/2q log(n/ε)),(where q>1), among them. In2006, Pan et al found by analysis, Newton direction of the self-regular proximity measure method used in the proof of the above conclusions, was through the "central equation" with an equivalent was idempotent transformation. Although the power function transformation from algebraic sense equivalent, but the speed to the optimal solution was not the same. Therefore, algebraic transformation based on proper, also can be reduced the computational complexity of primal-dual interior point algorithm.
Second, it is the feasible interior point algorithm in the initial iteration point selection is too demanding, not only to meet the strict equality constraints and nonnegative condition, and selecting the initial points in practical problems are hard to get, but infeasible interior point algorithm for relaxing the conditions, as long as it meets the nonnegative condition in the iteration begins, without the need to satisfy the equality constraints. This greatly reduces the difficulty in selecting the initial feasible point. Therefore, infeasible interior point algorithm in dealing with practical problems are widely used.
This paper is divided into two parts, theory and application. The first part, solve some theory problems of optimization algorithms mainly use the theory part; the second part, the application part is mainly used to solve some practical problems of optimization algorithm.
In the theory part, we firstly discussed the different neighborhood (based on large step size and small step size) for solving non-monotone linear complementary problem of higher order interior point algorithm. Secondly, ideas and framework of algebraically equivalent transformation based on KMM algorithm for linear complementarity problems, put forward a new primal-dual infeasible interior point algorithm, the global convergence of the algorithm. And the effectiveness of the algorithm is tested by numerical experiments. Finally, discussed based on kernel function to solve the infeasible interior point algorithm and prove its computational complexity and similar kernel function for solving nonlinear complementarity problem based on kernel function.
The second part is the application part, because that the complementarity problem is an important optimization problem, which is widely used in economic analysis, traffic equilibrium strategies of social economic model. So it is the very vital significance to research the study of complementarity problems. Therefore, the department based on economics theory as a foundation, discusses the application of linear complementary double matrix game problem in economics, and a collection of two typical double matrix game example (prisoner's dilemma game and inspect the game), potential function usd by linear complementarity problem and the descent method and path tracking algorithm the effective solution to test the above example.
Second is the use of cooperative mechanism of evolutionary game theory and optimization algorithm for rural cooperative organization, established heterogeneous groups of farmers (with organization and management ability and influence of the class and ordinary peasant class) in the evolution game model of operation of rural cooperative organization, in the previous round of cooperation according to the results, whether the cooperation game under the adjustment a round, gradually seek evolutionary stable equilibrium solution. In order to find the evolution stable equilibrium solution presents a new evolutionary algorithm. The basic idea of the algorithm is the combination of strategies space search space optimization problem is mapped to game theory in the objective function, the utility function is mapped to the game theory, the irrational game subject to local stable equilibrium state, according to local equilibrium Kobo subject to adjust their own strategy, the next round of the game, to search for better reach equilibrium, evolutionarily stable equilibrium solution, thus solving the evolutionary stable state of the actual problem.
引文
1.G.B.Dantig. Linear programming and extension[M].Princetton University Press.Princetion,1963.
2.L.G.Khachiyan.A polynomial algorithm in linear programming[J].Soviet Mathematics Doklady, 1979,20:191-194.
3.N.Karmarkar. A new polynomial-time algorithm for linear programming[J]. Combinatorica,1984,4 (5): 373-395.
4.马仲蕃.线性规划最新进展[M].科技出版社,1994.
5. D.Gay. A variant of Karmarkar's linear programming algorithm for problems in standard form[J]. Mathematical Programming.1987,37:81-90.
6.C.Gonzage. Polynomial affine algorithms for linear programming[J]. Mathematical Programming.1990, 49:7-21.
7.K.M.Ansreicher. Linear programming and Newton barrier flow[J]. Mathematical Programming.1988, 41:363-373.
8.M.J.Todd. Polynomial algorithm for linear programming. In Advances in Optimization and Control[J], Springer Verlag,Berlin.1988,13:49-66.
9.B.P.Burrell, M.J.Todd. The ellipsoid method generates dual variables[J]. Mathematics of Operation Research.1990,38:240-248.
10.Y.Ye. Interior point algorithm theory and analysis[M]. John Wiley and Sons, New York,1997.
11. S.J.Wright. Primal-dual interior-point methods[J]. Philadephia. SIAM.1997.
12.Y.Q.Wang. Primal-dual interior-point algorithms for semidefinite optimization based on a simple kernel function[J]. Journal of Mathematical modeling and algorithms.2005,4:409-433.
13.J.Peng, C.Roos, T.Terlaky. New and efficient large-update interior-point method for linear optimization[J]. Journal of Computation Technologies,2000,46 (1):61-80.
14.F.Huang,Y.Ye. An asymptiotical O((?)nL)-iteration path-following linear programming algorithm that uses wider neighborhood[J]. SIAM.J.Optimization,1996,6:570-586
15.J.Peng, C.Roos, T.Terlaky. Self-regular functions and new search directions for linear and semi-definite optimization[J]. Mathematical Programming,2002,93 (2):129-171
16.S.Pan, X.Li, S.he. An infeasible primal-dual interior point algorithm for linear programs based on logarithmic equivalent transformation[J]. Journal of mathematical analysis and applications,2006,314 (4):644-660
17. M.Salahi.The complexity of self-regular promity based infeasible IPMs[J].Technical Report 2003.
18-C.Roos. A full Newton step O(n) infeasible interior point algorithm for linear optimization[J].SIAM J.Optim,2006,16:1110-1136.
19.M.Kojima, N.Megiddo, S.Mizuno. A primal-dual infeasible-interior-point algorithm for linear programming[J]. Mathematical Programming.1993,61 (1):263-280
20.谢识予.经济博弈论[M].复旦大学出版社,2002.
21.龚小玉.非单调线性互补问题内点算法的研究.三峡大学硕士论文,2007.
22.C.Lemka. Biamatrix equilibrium points and mathematical programming[J]. Management Science, 1965,11:681-689.
23.R.Saigal. On the class of complementarity cones and Lemaka's algorithm[J]. SIAM J. On Applied Mathematics,1972,23:46-54.
24.R.W.Cottle, G.B.Dantzig. Complementarity pivot theory in mathematical programming[J]. Linear Algebra and its Applications,1968,1:103-125
25.R.W.Cottle, J.S.Pang. On solving linear complementarity problems as linear programs[J]. Mathematical Programming Study,1968,7:88-107.
26.P.M.Pardalos, J.B.Rosen. Global optimization approach to the linear complementarity problem[J].SiAM J.On scientific and statistical computing,1983,9:341-353.
27.O.L.Mangasarian. Characterization of linear complementarityproblems as linear programs[J]. Mathematical Programming Study,1978,7:74-87.
28.M.Kojima, N.Megiddo,T.Noma, A.Yoshise. A unified approach to interior point algorithms for linear complementarity problems[J]. Lecture Notes in Computer Science,Springer-Verlag, Berlin, New York,1991.
29.S.J.Wright. A path-following infeasible-interior-point algorithm for linear complementarity problems[J]. Optimization Methods and Software.1993,2:79-106.
30.S.J.Wright. An infeasible-interior-point algorithm for linear complementarity problems[J]. Mathematical Programming.1994,67(1):29-52
31.F.A.Potra. An O(nL) infeasible-interior-point algorithm for LCP with quadratic convergence[J]. Mathematical Programming.1994,67(3):219-240.
32.E.D. Andersen, Y.Ye. On homogeneous algorithm for the monotone complementarity problem[J]. Mathematical Programming.1999,84:375-399.
33.Y.Zhang. On the convergence of a class of infeasible-interior-point method for the horizontal linear complementarity problem[J]. SIAM.Optimization.1994,4:208-227.
34.P.Zhang, X.Li. An infeasible path-following methods for monotone LCPs[J]. Mathematical and Computer modeling.2003,38:23-31.
35.J.Wright. On reduced convex QP formulations of monotone LCPs[J]. Mathematical Programming. 2001,90:459-473.
36.L.Fernandes. An investigation of interior-point and block pivoting algorithms for large-scale symmetric monotone linear complementarity problems[J]. Computational Optimization and Applications.1996,5: 49-77.
37.B.Jansen., C.Roos, T.Terlaky. Improved complexity using high-order correctors for primal-dual Dikin affine scaling[J]. Math. Programming,1997,76:117-130.
38.M.Kojima, N.Megiddo, Yoshise. A primal-dual interior-point algorithm for linear programmingfJ]. Spring-Verlag, N.Y.,1989,6:29-47.
39.R.D.C.Monteiro, M.C.C.Resende. A polymomial-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension[J]. Mathematics of Operations Research,1990,15:191-214.
40.Y.B.Zhao. Enlarging neighborhoods of interior-point algorithms for linear programming via least values of proximity measure functions[J]. Applied numerical Mathematics,2006,2:1236-1345.
41.F.A.Potra. A superlinearly convergent predictor-corrector methods for degrade LCP in a wide neighborhood of the central path with O((?)nL)-iteration complexity[J]. Mathematical Programming, 2004,100:317-337.
42.G.Thao, J.Sun. On the rate of local convergence of high-order infeasible path following algorithm[J]. Computational Operations Research,1999,14(3):293-307.
43.M.W.Zhang,C.C.Huang.A high-order affine scaling algorithm for a class of nonmontonic linear complementarity problems[J]. Mathematica Numerica Sinica,2004,26 (1):37-46.
44.B.Jansen, C.Roos, T.Terlaky. A polynomial primal-dual Dikin-type algorithm for linear programming[J]. Mathematics of Operations Research,1996,21:341-353.
45.M.Kojima, N.Megiddo, Y.Ye. An interior-point potential reduction algorithm for the linear complementary problem. Mathematics of Operations Research,1992 (54):267-279
46.张明望.一类非单调线性互补问题的高阶Dikin型仿射尺度算法[J],数学杂志,2004,24(5)：585-590.
47.J.Miao. A quadratically convergent O((κ+1)(?)nL)-iteration algorithm for the P* (κ)-matrix linear complementarity problem[J]. Mathematical Programming,1995,69:355-368.
48.F.A.Potra, GR.Sheng. Predictor-corrector algorithm for solving P*(κ)-matrix LCP from arbitrary positive starting points[J]. Mathematical Programming,1996,76:223-244.
49.R.Monteiro, I.Alder, M.C.C.Resencle. A polynomicl-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension[J]. Mathematics of Operations Research,1990,15(1):191-198.
50.Y.B.Zhao, J.Y.Han. Two interior-point methods for nonlinear complementarity problems[J]. Computational Optimization and Applications,1999,102:659-679.
51.L.Tungel. On the convergence of primal-dual interior-point methods with wide neighborhoods [J]. Computional optimizational and Applications,1995,4:139-158.
52.F.A.Potra. Corrector-predictor methods for monotone linear complementarity problems in a wide neighborhood of the central path[J]. Mathematical Programming,2006,1:1436-1446.
53.Lustig. Feasible issues in a primal-dual interior point method[J].Mathematical programming,1990,67:145-162.
54.K.Tanabe. Centered Newton method for linear programming;Interior and 'exterior' point method[J]. IN:New Method for Linear Programming.1990,3:98-100.
55.Y.Zhang, D.Zhang. Superlinear convergence of infeasible interior-point methods for linear programming[J]. Mathematical programming,1994,66(5):36-377.
56.Mizuno S. Polynomiality of infeasible interior-point algorithm for linear programming[J]. Mathematical Programming,1997,67(2):109-119.
57.Yu.Nesterov,M.J.Todd.Infeasible start primal-dual methods and infeasiblity detectors for nonlinear programming problem[J].Mathematical Programming,1999,84:227-267.
58.J.Peng,C.Roos.Self-Regularity.A New Paradigm for primal dual interior point algorithm [M],Princeton University Press,2002.
59.Vanderbei. Linear Programming:Foundations and Extensions[M]. Kluwer Academic Publishers.Boston,USA,1996.
60.J.Korzak. Convergence analysis of inexact infeasible-interior-point algorithm for linear programming[M]. SIAM Journal on Optimization,2000,11:133-148.
61.Y.Q.Bai,C.Roos. A comparative study of kernel functions for primal-dual interior point algotirhms in linear optimization[J].SIAM J.Optim,2004,15:101-128.
62.K.G.Murty. Linear complementarity, Linear and Nonlinear Programming. Sigma.Ser.Appl.Math.3, Heldermann-verlag,Berlin,1988.
63.H.Ahn. Iterative methods for linear complementarity problem with uperbounds and lowerbounds[J]. Mathematical Programming,1983,26:265-398
64.H.Mansouri,C.Roos. A new full Newton step on infeasible interior point algorithm for linear programming [J]. Numer.Algorithms,2009,52:225-255.
65.Y.Zhang. On the convergence of a class of infeasible interior point methods for the horizontal linear complementarity problem[J]. SIAM J.Optim,1994,4:208-227.
65.Min-Kyung Kim, Gyeong-Mi Cho. Interior point algorithm for P* nonlinear complementarity problems[J]. Journal of computational and applied mathematics,2011.
66.Liying Liu,Shaoyong Li. A new kind of simple kernel function yielding good iteration bounds for primal-dual interior point methods[J]. Journal of computational and applied mathematics,2011.,235:2944-2955.
67.H.Mansouri,M.Zangiabadi,M.Pirhaji.A full-Newton step O(n) infeasible interior point algorithm for linear complementarity problems[J]. Nonlinear Anaylsis:Real World Applications,2011,12:545-561.
68.王然,异质寡头企业的古诺竞争与百川德竞争,山东大学硕士论文,2010.
69.李佳.基于博弈理论的招标问题建模与优化方法的研究,沈阳工业大学硕士论文,2008.
70.Nash J F. The bargaining problem[J].Econoics,1995,18:155-162.
70.胡运权.运筹学教程[M]。清华大学出版社,2003.
71.张艳.基于博弈论的流域水资源配置研究,扬州大学硕士论文,2009.
72.冯丽荣.互补问题在经济中的应用,北京交通大学硕士学位论文。2010.
73.王先甲,全吉,刘伟兵.有限理性下的演化博弈与合作机制研究[J].系统工程理论与实践,2011,31：82-93..
74.叶俊.基于博弈论的背包问题优化算法[J].华中科技大学学报,2003,12：53-55.
75.李兴隆.背包问题及其算法研究,硅谷,2008.
76.李武.农村社会化服务组织的合作机制研究,南昌大学博士论文,2009.
77.王征兵,许婕,孙浩杰.国外发展农民专业合作社的经验及其借鉴[J],湖南农业大学学报(社会科学版),2010,11(2)：61-65.
78.王曙光著.守望田野——农村金融田野调查手记[M].中国发展出版社,2010.
79.邓衡山.中国农民专业合作经济组织发展现状及制约因素分析[J]——基于全国7省760个村的大样本调查[J],现代经济探讨,2010,55-59.
80.苏晓云.贫困地区农民合作经济组织实证研究——基于广西凤山县的调查与思考[J],毛泽东、邓小平理论研究,88-95.
81.曹海林.失衡的引擎：农民经济合作组织发展困境之根[J]社会科学研究[J],2012,6：45-46.
82.李昱姣.合作悖论：农民经济合作的财力资源要求与自身能力的不足[J],社会主义研究2010,2.
83.任军利.中韩两国农民合作组织的比较及其启示[J],广东农业科学,2012,2：44-46.
84.吴雄周.农业合作组织发展能力的形成、演化和培育：基于自组织理论视角[J],湖南社会科学。2012,5：11-13.
85.高杰.基于不完全契约理论的农业准一体化经营组织分析[J],经济问题探索2013,1：78-92.
86.侯志阳.农村社会管理体制创新与农村公共服务供给[J],南京航空航天大学学报(社会科学版)2011,5：15-19.
87.巩玉涛.农村社会组织参与基本公共服务供给模式研究[J],广东农业科学2012,21：13-15.
88.徐顽强.社会管理创新视角下农村社会组织发展困境和路径研究[J],广西社会科学2012,6：45-50.
89.张翠娥.社会性别视角下的农民组织化——基于武汉市新洲区的调查[J],妇女研究论丛2012,2：14-20.
90.阎占定.新型农民合作经济组织参与乡村治理的经济分析[J],郑州大学学报2012,2：15-18.
91.徐勇.农村社区治理主体及其权力关系分析[J],理论月刊2013,1：45-49.
92.高强.日本农地制度改革及对我国的启示[J],调研世界20120,5：89-92.
93.黄祖辉.我国农业产业化经营机制要创新——发挥农户经营、合作经营、公司经营三大制度优势[J],农村经营管理2011,08：78-80.
94.施晟.“农超对接”进程中农产品供应链的合作绩效与剩余分配——基于“农户+合作社+超市”模式的分析[J],中国农村观察2012,04：62-65.
95.李玉新.基于产业协同与城乡统筹的乡村旅游转型路径——以山东省寿光市、蓬莱市、长岛县为例[J],哈尔滨商业大学学报2012,06：32-36.
96.李佳.河北省新农保制度的激励机制研究[J],人口与经济2012,02：61-66.
97.杨丹.农业分工和专业化能否引致农户的合作行为——基于西部5省20县农户数据的实证分析[J],农业技术经济2012,02：78-91.
98.黄家亮.社会资源配置模式变迁与社区服务发展新趋势——基于北京市社区服务实践探索的分析[J],社会主义研究2012,03：78-90.
99.马华.农民合作中外部力量的作用机理——对“南农实验”宗族合作与理性互动的考察[J],社会主义研究2012,06：12-14.
100.刘漠炎.培育壮大县域经济统筹城乡协调发展[J],当代江西2007,12：14-16.
101.孙亚范.农民专业合作社成员合作意愿及影响因素分析[J],2012,06：60-63.
102.孔祥智.建立新型农业社会化服务体系：必要性、模式选择和对策建议[J],教学与研究2012,01.
103.陈家涛,基于博弈论视角的农户合作行为分析[J],经济问题2010,03：81-84.
104.杨红炳.基于博弈论的合作社成员风险防范投资与激励问题研究[J],统计与决策2012,02：16-19.
105.顾艳红.,博弈视角下林业合作组织的违约金机制研究——以“公司+林业合作组织+林农”模式为例[J],林业经济问题,2012.02：52-55.
106.罗倩文.基于演化视角的农民合作经济组织稳定性分析[J],农机化研究,2011.02：56-58.
107.胡振鹏.农民水利协会的合作机制研究[J],自然资源学报,2009,02：32-36.
108.王军.中国农民专业合作社社员机会主义行为的约束机制分析[J],中国农村观察,2011,05：26-28.
109.赵佳.农民专业合作社的经营方式转变与组织制度创新：皖省例证[J]改革,2013.01：62-65.
110.曹锦清.黄河边的中国——一个学者对乡村社会的观察与思考,上海文艺出版社,2000.
111.刘谟炎.农民长久合作——万载百年鲤陂水利协会研究,中国农业出版社,2011
112.罗伯特.阿克塞尔罗德.合作的进化[M],上海世纪出版集团,2005.
2.L.G.Khachiyan.A polynomial algorithm in linear programming[J].Soviet Mathematics Doklady, 1979,20:191-194.
3.N.Karmarkar. A new polynomial-time algorithm for linear programming[J]. Combinatorica,1984,4 (5): 373-395.
4.马仲蕃.线性规划最新进展[M].科技出版社,1994.
5. D.Gay. A variant of Karmarkar's linear programming algorithm for problems in standard form[J]. Mathematical Programming.1987,37:81-90.
6.C.Gonzage. Polynomial affine algorithms for linear programming[J]. Mathematical Programming.1990, 49:7-21.
7.K.M.Ansreicher. Linear programming and Newton barrier flow[J]. Mathematical Programming.1988, 41:363-373.
8.M.J.Todd. Polynomial algorithm for linear programming. In Advances in Optimization and Control[J], Springer Verlag,Berlin.1988,13:49-66.
9.B.P.Burrell, M.J.Todd. The ellipsoid method generates dual variables[J]. Mathematics of Operation Research.1990,38:240-248.
10.Y.Ye. Interior point algorithm theory and analysis[M]. John Wiley and Sons, New York,1997.
11. S.J.Wright. Primal-dual interior-point methods[J]. Philadephia. SIAM.1997.
12.Y.Q.Wang. Primal-dual interior-point algorithms for semidefinite optimization based on a simple kernel function[J]. Journal of Mathematical modeling and algorithms.2005,4:409-433.
13.J.Peng, C.Roos, T.Terlaky. New and efficient large-update interior-point method for linear optimization[J]. Journal of Computation Technologies,2000,46 (1):61-80.
14.F.Huang,Y.Ye. An asymptiotical O((?)nL)-iteration path-following linear programming algorithm that uses wider neighborhood[J]. SIAM.J.Optimization,1996,6:570-586
15.J.Peng, C.Roos, T.Terlaky. Self-regular functions and new search directions for linear and semi-definite optimization[J]. Mathematical Programming,2002,93 (2):129-171
16.S.Pan, X.Li, S.he. An infeasible primal-dual interior point algorithm for linear programs based on logarithmic equivalent transformation[J]. Journal of mathematical analysis and applications,2006,314 (4):644-660
17. M.Salahi.The complexity of self-regular promity based infeasible IPMs[J].Technical Report 2003.
18-C.Roos. A full Newton step O(n) infeasible interior point algorithm for linear optimization[J].SIAM J.Optim,2006,16:1110-1136.
19.M.Kojima, N.Megiddo, S.Mizuno. A primal-dual infeasible-interior-point algorithm for linear programming[J]. Mathematical Programming.1993,61 (1):263-280
20.谢识予.经济博弈论[M].复旦大学出版社,2002.
21.龚小玉.非单调线性互补问题内点算法的研究.三峡大学硕士论文,2007.
22.C.Lemka. Biamatrix equilibrium points and mathematical programming[J]. Management Science, 1965,11:681-689.
23.R.Saigal. On the class of complementarity cones and Lemaka's algorithm[J]. SIAM J. On Applied Mathematics,1972,23:46-54.
24.R.W.Cottle, G.B.Dantzig. Complementarity pivot theory in mathematical programming[J]. Linear Algebra and its Applications,1968,1:103-125
25.R.W.Cottle, J.S.Pang. On solving linear complementarity problems as linear programs[J]. Mathematical Programming Study,1968,7:88-107.
26.P.M.Pardalos, J.B.Rosen. Global optimization approach to the linear complementarity problem[J].SiAM J.On scientific and statistical computing,1983,9:341-353.
27.O.L.Mangasarian. Characterization of linear complementarityproblems as linear programs[J]. Mathematical Programming Study,1978,7:74-87.
28.M.Kojima, N.Megiddo,T.Noma, A.Yoshise. A unified approach to interior point algorithms for linear complementarity problems[J]. Lecture Notes in Computer Science,Springer-Verlag, Berlin, New York,1991.
29.S.J.Wright. A path-following infeasible-interior-point algorithm for linear complementarity problems[J]. Optimization Methods and Software.1993,2:79-106.
30.S.J.Wright. An infeasible-interior-point algorithm for linear complementarity problems[J]. Mathematical Programming.1994,67(1):29-52
31.F.A.Potra. An O(nL) infeasible-interior-point algorithm for LCP with quadratic convergence[J]. Mathematical Programming.1994,67(3):219-240.
32.E.D. Andersen, Y.Ye. On homogeneous algorithm for the monotone complementarity problem[J]. Mathematical Programming.1999,84:375-399.
33.Y.Zhang. On the convergence of a class of infeasible-interior-point method for the horizontal linear complementarity problem[J]. SIAM.Optimization.1994,4:208-227.
34.P.Zhang, X.Li. An infeasible path-following methods for monotone LCPs[J]. Mathematical and Computer modeling.2003,38:23-31.
35.J.Wright. On reduced convex QP formulations of monotone LCPs[J]. Mathematical Programming. 2001,90:459-473.
36.L.Fernandes. An investigation of interior-point and block pivoting algorithms for large-scale symmetric monotone linear complementarity problems[J]. Computational Optimization and Applications.1996,5: 49-77.
37.B.Jansen., C.Roos, T.Terlaky. Improved complexity using high-order correctors for primal-dual Dikin affine scaling[J]. Math. Programming,1997,76:117-130.
38.M.Kojima, N.Megiddo, Yoshise. A primal-dual interior-point algorithm for linear programmingfJ]. Spring-Verlag, N.Y.,1989,6:29-47.
39.R.D.C.Monteiro, M.C.C.Resende. A polymomial-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension[J]. Mathematics of Operations Research,1990,15:191-214.
40.Y.B.Zhao. Enlarging neighborhoods of interior-point algorithms for linear programming via least values of proximity measure functions[J]. Applied numerical Mathematics,2006,2:1236-1345.
41.F.A.Potra. A superlinearly convergent predictor-corrector methods for degrade LCP in a wide neighborhood of the central path with O((?)nL)-iteration complexity[J]. Mathematical Programming, 2004,100:317-337.
42.G.Thao, J.Sun. On the rate of local convergence of high-order infeasible path following algorithm[J]. Computational Operations Research,1999,14(3):293-307.
43.M.W.Zhang,C.C.Huang.A high-order affine scaling algorithm for a class of nonmontonic linear complementarity problems[J]. Mathematica Numerica Sinica,2004,26 (1):37-46.
44.B.Jansen, C.Roos, T.Terlaky. A polynomial primal-dual Dikin-type algorithm for linear programming[J]. Mathematics of Operations Research,1996,21:341-353.
45.M.Kojima, N.Megiddo, Y.Ye. An interior-point potential reduction algorithm for the linear complementary problem. Mathematics of Operations Research,1992 (54):267-279
46.张明望.一类非单调线性互补问题的高阶Dikin型仿射尺度算法[J],数学杂志,2004,24(5)：585-590.
47.J.Miao. A quadratically convergent O((κ+1)(?)nL)-iteration algorithm for the P* (κ)-matrix linear complementarity problem[J]. Mathematical Programming,1995,69:355-368.
48.F.A.Potra, GR.Sheng. Predictor-corrector algorithm for solving P*(κ)-matrix LCP from arbitrary positive starting points[J]. Mathematical Programming,1996,76:223-244.
49.R.Monteiro, I.Alder, M.C.C.Resencle. A polynomicl-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension[J]. Mathematics of Operations Research,1990,15(1):191-198.
50.Y.B.Zhao, J.Y.Han. Two interior-point methods for nonlinear complementarity problems[J]. Computational Optimization and Applications,1999,102:659-679.
51.L.Tungel. On the convergence of primal-dual interior-point methods with wide neighborhoods [J]. Computional optimizational and Applications,1995,4:139-158.
52.F.A.Potra. Corrector-predictor methods for monotone linear complementarity problems in a wide neighborhood of the central path[J]. Mathematical Programming,2006,1:1436-1446.
53.Lustig. Feasible issues in a primal-dual interior point method[J].Mathematical programming,1990,67:145-162.
54.K.Tanabe. Centered Newton method for linear programming;Interior and 'exterior' point method[J]. IN:New Method for Linear Programming.1990,3:98-100.
55.Y.Zhang, D.Zhang. Superlinear convergence of infeasible interior-point methods for linear programming[J]. Mathematical programming,1994,66(5):36-377.
56.Mizuno S. Polynomiality of infeasible interior-point algorithm for linear programming[J]. Mathematical Programming,1997,67(2):109-119.
57.Yu.Nesterov,M.J.Todd.Infeasible start primal-dual methods and infeasiblity detectors for nonlinear programming problem[J].Mathematical Programming,1999,84:227-267.
58.J.Peng,C.Roos.Self-Regularity.A New Paradigm for primal dual interior point algorithm [M],Princeton University Press,2002.
59.Vanderbei. Linear Programming:Foundations and Extensions[M]. Kluwer Academic Publishers.Boston,USA,1996.
60.J.Korzak. Convergence analysis of inexact infeasible-interior-point algorithm for linear programming[M]. SIAM Journal on Optimization,2000,11:133-148.
61.Y.Q.Bai,C.Roos. A comparative study of kernel functions for primal-dual interior point algotirhms in linear optimization[J].SIAM J.Optim,2004,15:101-128.
62.K.G.Murty. Linear complementarity, Linear and Nonlinear Programming. Sigma.Ser.Appl.Math.3, Heldermann-verlag,Berlin,1988.
63.H.Ahn. Iterative methods for linear complementarity problem with uperbounds and lowerbounds[J]. Mathematical Programming,1983,26:265-398
64.H.Mansouri,C.Roos. A new full Newton step on infeasible interior point algorithm for linear programming [J]. Numer.Algorithms,2009,52:225-255.
65.Y.Zhang. On the convergence of a class of infeasible interior point methods for the horizontal linear complementarity problem[J]. SIAM J.Optim,1994,4:208-227.
65.Min-Kyung Kim, Gyeong-Mi Cho. Interior point algorithm for P* nonlinear complementarity problems[J]. Journal of computational and applied mathematics,2011.
66.Liying Liu,Shaoyong Li. A new kind of simple kernel function yielding good iteration bounds for primal-dual interior point methods[J]. Journal of computational and applied mathematics,2011.,235:2944-2955.
67.H.Mansouri,M.Zangiabadi,M.Pirhaji.A full-Newton step O(n) infeasible interior point algorithm for linear complementarity problems[J]. Nonlinear Anaylsis:Real World Applications,2011,12:545-561.
68.王然,异质寡头企业的古诺竞争与百川德竞争,山东大学硕士论文,2010.
69.李佳.基于博弈理论的招标问题建模与优化方法的研究,沈阳工业大学硕士论文,2008.
70.Nash J F. The bargaining problem[J].Econoics,1995,18:155-162.
70.胡运权.运筹学教程[M]。清华大学出版社,2003.
71.张艳.基于博弈论的流域水资源配置研究,扬州大学硕士论文,2009.
72.冯丽荣.互补问题在经济中的应用,北京交通大学硕士学位论文。2010.
73.王先甲,全吉,刘伟兵.有限理性下的演化博弈与合作机制研究[J].系统工程理论与实践,2011,31：82-93..
74.叶俊.基于博弈论的背包问题优化算法[J].华中科技大学学报,2003,12：53-55.
75.李兴隆.背包问题及其算法研究,硅谷,2008.
76.李武.农村社会化服务组织的合作机制研究,南昌大学博士论文,2009.
77.王征兵,许婕,孙浩杰.国外发展农民专业合作社的经验及其借鉴[J],湖南农业大学学报(社会科学版),2010,11(2)：61-65.
78.王曙光著.守望田野——农村金融田野调查手记[M].中国发展出版社,2010.
79.邓衡山.中国农民专业合作经济组织发展现状及制约因素分析[J]——基于全国7省760个村的大样本调查[J],现代经济探讨,2010,55-59.
80.苏晓云.贫困地区农民合作经济组织实证研究——基于广西凤山县的调查与思考[J],毛泽东、邓小平理论研究,88-95.
81.曹海林.失衡的引擎：农民经济合作组织发展困境之根[J]社会科学研究[J],2012,6：45-46.
82.李昱姣.合作悖论：农民经济合作的财力资源要求与自身能力的不足[J],社会主义研究2010,2.
83.任军利.中韩两国农民合作组织的比较及其启示[J],广东农业科学,2012,2：44-46.
84.吴雄周.农业合作组织发展能力的形成、演化和培育：基于自组织理论视角[J],湖南社会科学。2012,5：11-13.
85.高杰.基于不完全契约理论的农业准一体化经营组织分析[J],经济问题探索2013,1：78-92.
86.侯志阳.农村社会管理体制创新与农村公共服务供给[J],南京航空航天大学学报(社会科学版)2011,5：15-19.
87.巩玉涛.农村社会组织参与基本公共服务供给模式研究[J],广东农业科学2012,21：13-15.
88.徐顽强.社会管理创新视角下农村社会组织发展困境和路径研究[J],广西社会科学2012,6：45-50.
89.张翠娥.社会性别视角下的农民组织化——基于武汉市新洲区的调查[J],妇女研究论丛2012,2：14-20.
90.阎占定.新型农民合作经济组织参与乡村治理的经济分析[J],郑州大学学报2012,2：15-18.
91.徐勇.农村社区治理主体及其权力关系分析[J],理论月刊2013,1：45-49.
92.高强.日本农地制度改革及对我国的启示[J],调研世界20120,5：89-92.
93.黄祖辉.我国农业产业化经营机制要创新——发挥农户经营、合作经营、公司经营三大制度优势[J],农村经营管理2011,08：78-80.
94.施晟.“农超对接”进程中农产品供应链的合作绩效与剩余分配——基于“农户+合作社+超市”模式的分析[J],中国农村观察2012,04：62-65.
95.李玉新.基于产业协同与城乡统筹的乡村旅游转型路径——以山东省寿光市、蓬莱市、长岛县为例[J],哈尔滨商业大学学报2012,06：32-36.
96.李佳.河北省新农保制度的激励机制研究[J],人口与经济2012,02：61-66.
97.杨丹.农业分工和专业化能否引致农户的合作行为——基于西部5省20县农户数据的实证分析[J],农业技术经济2012,02：78-91.
98.黄家亮.社会资源配置模式变迁与社区服务发展新趋势——基于北京市社区服务实践探索的分析[J],社会主义研究2012,03：78-90.
99.马华.农民合作中外部力量的作用机理——对“南农实验”宗族合作与理性互动的考察[J],社会主义研究2012,06：12-14.
100.刘漠炎.培育壮大县域经济统筹城乡协调发展[J],当代江西2007,12：14-16.
101.孙亚范.农民专业合作社成员合作意愿及影响因素分析[J],2012,06：60-63.
102.孔祥智.建立新型农业社会化服务体系：必要性、模式选择和对策建议[J],教学与研究2012,01.
103.陈家涛,基于博弈论视角的农户合作行为分析[J],经济问题2010,03：81-84.
104.杨红炳.基于博弈论的合作社成员风险防范投资与激励问题研究[J],统计与决策2012,02：16-19.
105.顾艳红.,博弈视角下林业合作组织的违约金机制研究——以“公司+林业合作组织+林农”模式为例[J],林业经济问题,2012.02：52-55.
106.罗倩文.基于演化视角的农民合作经济组织稳定性分析[J],农机化研究,2011.02：56-58.
107.胡振鹏.农民水利协会的合作机制研究[J],自然资源学报,2009,02：32-36.
108.王军.中国农民专业合作社社员机会主义行为的约束机制分析[J],中国农村观察,2011,05：26-28.
109.赵佳.农民专业合作社的经营方式转变与组织制度创新：皖省例证[J]改革,2013.01：62-65.
110.曹锦清.黄河边的中国——一个学者对乡村社会的观察与思考,上海文艺出版社,2000.
111.刘谟炎.农民长久合作——万载百年鲤陂水利协会研究,中国农业出版社,2011
112.罗伯特.阿克塞尔罗德.合作的进化[M],上海世纪出版集团,2005.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |