具广义锥凸集值映射的集值优化问题的Global真有效解的最优条件
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摘要
在实赋范空间中讨论集值优化问题的Global真有效解的最优性条件。首先在实赋范空间中给出集值优化问题Global真有效解的概念,其次借助于切上图导数建立了具广义锥-凸集值映射的集值优化问题的Global真有效解的Kuhn-Tucker型最优性条件。
The optimality conditions of global proper efficient solutions for set-valued optimization problems in real normed spaces are investigated.Firstly,the concepts of Global proper efficient solutions for set-valued optimization problem in real normed spaces is given.Secondly,the Kuhn-Tucker type optimality conditions for global proper efficient solutions of set-valued optimization problem with generalized cone-convex set-valued mappings are established by means of contingent epiderivative.
The optimality conditions of global proper efficient solutions for set-valued optimization problems in real normed spaces are investigated.Firstly,the concepts of Global proper efficient solutions for set-valued optimization problem in real normed spaces is given.Secondly,the Kuhn-Tucker type optimality conditions for global proper efficient solutions of set-valued optimization problem with generalized cone-convex set-valued mappings are established by means of contingent epiderivative.
引文
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[7] GONG X H,DONG H B,WANG S Y.Optimality Conditions for Proper Efficient Solutions of Vector Set-valued Optimization[J].J Math Anal Appl,2003,284:332-350.
[8] QIU J H.Cone-directed Contingent Derivatives and Generalized Preinrex Set-valued Optimization[J].Acta Mathmatical Scientia,2007,27:211-218.
[9] QIU Q S.The Generalized Convexity of Set-valued Maps and Set-valued Optimization[J].Doctoral Thesis Shang Hai University,2009.
[10] ZHONG Z A,YANG X M,QIU Q S.Optimality Conditions of the Set-valued Optimization Problem with Generalized Cone Convex Set-valued Maps Characterized by Contingent Epi derivative[J].Acta Mathematical Applicatae Sinica English series,2018,34(1):11-18.
[11] 孟旭东,王三华,邓中书.含参集值向量均衡问题有效解映射的下半连续性[J].南昌大学学报(理科版),2016,40(3):219-224.
[12] 孟旭东,王三华.含参集值向量均衡问题各种有效解映射的下半连续性[J].数学的实践与认识,2017,47(5):234-241.
[13] 孟旭东,王三华.含参广义集值优化问题解集映射的连续性[J].吉林大学学报(理学版),2018,56(4):830-835.
[2] Corley H W.Existence and Lagrange Duality for Maximization of Set-valued Functions[J].J Optim Theory Appl,1987,54:489-501.
[3] JAHN J,RAUH R.Contingent Epiderivatives and Set-Valued Optimization[J].Math Methods Oper Res,1997,46:193-211.
[4] CHEN,G Y,JAHN,J.Optimality Conditions for Set-valued Optimization Problems[J].Math Methods Oper Res,1998,48:187-200.
[5] LIU W,GONG X H.Proper Efficiency for Set-valued Vector Optimization Problems and Vector Variational Inequalities[J].Math Methods Oper Res,2000,51:443-457.
[6] HUANG Y W.Generalized Constraint Qualifications and Optimality Conditions for Set-valued Optimization Problems[J].J.Math Aual Appl,2002,265:309-321.
[7] GONG X H,DONG H B,WANG S Y.Optimality Conditions for Proper Efficient Solutions of Vector Set-valued Optimization[J].J Math Anal Appl,2003,284:332-350.
[8] QIU J H.Cone-directed Contingent Derivatives and Generalized Preinrex Set-valued Optimization[J].Acta Mathmatical Scientia,2007,27:211-218.
[9] QIU Q S.The Generalized Convexity of Set-valued Maps and Set-valued Optimization[J].Doctoral Thesis Shang Hai University,2009.
[10] ZHONG Z A,YANG X M,QIU Q S.Optimality Conditions of the Set-valued Optimization Problem with Generalized Cone Convex Set-valued Maps Characterized by Contingent Epi derivative[J].Acta Mathematical Applicatae Sinica English series,2018,34(1):11-18.
[11] 孟旭东,王三华,邓中书.含参集值向量均衡问题有效解映射的下半连续性[J].南昌大学学报(理科版),2016,40(3):219-224.
[12] 孟旭东,王三华.含参集值向量均衡问题各种有效解映射的下半连续性[J].数学的实践与认识,2017,47(5):234-241.
[13] 孟旭东,王三华.含参广义集值优化问题解集映射的连续性[J].吉林大学学报(理学版),2018,56(4):830-835.