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1.
Efficiency and Henig Efficiency for Vector Equilibrium Problems 总被引:6,自引:0,他引:6
We introduce the concept of Henig efficiency for vector equilibrium problems, and extend scalarization results from vector optimization problems to vector equilibrium problems. Using these scalarization results, we discuss the existence of the efficient solutions and the connectedness of the set of Henig efficient solutions to the vector-valued Hartman–Stampacchia variational inequality. 相似文献
2.
龙宪军 《数学物理学报(A辑)》2014,34(3):593-602
在Asplund空间中,研究了非凸向量均衡问题近似解的最优性条件.借助Mordukhovich次可微概念,在没有任何凸性条件下获得了向量均衡问题εe-拟弱有效解,εe-拟Henig有效解,εe-拟全局有效解以及εe-拟有效解的必要最优性条件.作为它的应用,还给出了非凸向量优化问题近似解的最优性条件. 相似文献
3.
该文讨论局部凸空间中的约束集值优化问题. 首先, 在生成锥内部凸-锥-类凸假设下, 建立了Henig真有效解在标量化和Lagrange乘子意义下的最优性条件. 其次, 对集值Lagrange映射引入Henig真鞍点的概念, 并用这一概念刻画了Henig真有效解. 最后, 引入了一个标量Lagrange对偶模型, 并得到了关于Henig真有效解的对偶定理. 另外, 该文所得结果均不需要约束序锥有非空的内部. 相似文献
4.
Jing Hui QIU 《数学学报(英文版)》2009,25(3):445-454
Applying the theory of locally convex spaces to vector optimization, we investigate the relationship between Henig proper efficient points and generalized Henig proper efficient points. In particular, we obtain a sufficient and necessary condition for generalized Henig proper efficient points to be Henig proper efficient points. From this, we derive several convenient criteria for judging Henig proper efficient points. 相似文献
5.
Henig Efficiency in Vector Optimization with Nearly Cone-subconvexlike Set-valued Functions 总被引:1,自引:0,他引:1
Qiu-sheng Qiu 《应用数学学报(英文版)》2007,23(2):319-328
In this paper,we study Henig efficiency in vector optimization with nearly cone-subconvexlikeset-valued function.The existence of Henig efficient point is proved and characterization of Henig efficiencyis established using the method of Lagrangian multiplier.As an interesting application of the results in thispaper,we establish a Lagrange multiplier theorem for super efficiency in vector optimization with nearly cone-subconvexlike set-valued function. 相似文献
6.
Xun-Hua Gong 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(11):3598-3612
In this paper, we investigated vector equilibrium problems and gave the scalarization results for weakly efficient solutions, Henig efficient solutions, and globally efficient solutions to the vector equilibrium problems without the convexity assumption. Using nonsmooth analysis and the scalarization results, we provided the necessary conditions for weakly efficient solutions, Henig efficient solutions, globally efficient solutions, and superefficient solutions to vector equilibrium problems. By the assumption of convexity, we gave sufficient conditions for those solutions. As applications, we gave the necessary and sufficient conditions for corresponding solutions to vector variational inequalities and vector optimization problems. 相似文献
7.
Tran Van Su 《4OR: A Quarterly Journal of Operations Research》2018,16(2):173-198
This article presents necessary and sufficient optimality conditions for weakly efficient solution, Henig efficient solution, globally efficient solution and superefficient solution of vector equilibrium problem without constraints in terms of contingent derivatives in Banach spaces with stable functions. Using the steadiness and stability on a neighborhood of optimal point, necessary optimality conditions for efficient solutions are derived. Under suitable assumptions on generalized convexity, sufficient optimality conditions are established. Without assumptions on generalized convexity, a necessary and sufficient optimality condition for efficient solutions of unconstrained vector equilibrium problem is also given. Many examples to illustrate for the obtained results in the paper are derived as well. 相似文献
8.
文章证明了严有效点等价于Henig真有效点.利用这个等价关系,得到了局部凸空间中Henig真有效点的存在性条件。纯量化特征和稠密性定理.并且改进了已知的有关结果. 相似文献
9.
Yu Han 《Optimization》2016,65(2):357-367
In this paper, we establish the connectedness of the sets of Henig efficient solutions, globally efficient solutions, weak efficient solutions, superefficient solutions and efficient solutions for a class of generalized vector equilibrium problems without the assumptions of monotonicity and compactness. 相似文献
10.
11.
该文在赋范线性空间中对集值映射引入锥- Henig有效次梯度和锥- Henig有效次 微分的概念. 借助凸集分离定理证明了锥- Henig有效次微分的存在性, 并且建立了线性泛函为锥- Henig有效次梯度的充要条件. 最后, 对于一类参数 扰动集值优化问题讨论了其在Henig有效意义下的稳定性. 相似文献
12.
In this paper, a generalized vector equilibrium problem is introduced and studied. A scalar characterization of weak efficient
solutions for the generalized vector equilibrium problem is obtained. By using the scalarization result, the existence of
the weak efficient solutions and the connectedness of the set of weak efficient solutions for the generalized vector equilibrium
problem are proved in locally convex spaces. 相似文献
13.
Xun-Hua Gong 《Journal of Mathematical Analysis and Applications》2005,307(1):12-31
In this paper, we consider the set-valued vector optimization problems with constraint in locally convex spaces. We present the necessary and sufficient conditions for Henig efficient solution pair, globally proper efficient solution pair and super efficient solution pair without the ordering cones having the nonempty interior. 相似文献
14.
Q. L. Wang 《Numerical Functional Analysis & Optimization》2013,34(1):94-112
In this article, by using the generalized second-order contingent (adjacent) epiderivatives of set-valued maps, we obtain necessary optimality conditions and sufficient optimality conditions for weakly efficient solutions, Henig efficient solutions to the set-valued vector equilibrium problems with constraints. Some results of this article improve the corresponding results in literatures by lessening the assumption of convexity. 相似文献
15.
AbstractNecessary optimality conditions for local Henig efficient and superefficient solutions of vector equilibrium problems involving equality, inequality, and set constraints in Banach space with locally Lipschitz functions are established under a suitable constraint qualification via the Michel–Penot subdifferentials. With assumptions on generalized convexity, necessary conditions for Henig efficiency and superefficiency become sufficient ones. Some applications to vector variational inequalities and vector optimization problems are given as well. 相似文献
16.
《Optimization》2012,61(1):155-165
In this article, we study well-posedness and stability aspects for vector optimization in terms of minimizing sequences defined using the notion of Henig proper efficiency. We justify the importance of set convergence in the study of well-posedness of vector problems by establishing characterization of well-posedness in terms of upper Hausdorff convergence of a minimizing sequence of sets to the set of Henig proper efficient solutions. Under certain compactness assumptions, a convex vector optimization problem is shown to be well-posed. Finally, the stability of vector optimization is discussed by considering a perturbed problem with the objective function being continuous. By assuming the upper semicontinuity of certain set-valued maps associated with the perturbed problem, we establish the upper semicontinuity of the solution map. 相似文献
17.
Connectedness of the Solution Sets and Scalarization for Vector Equilibrium Problems 总被引:3,自引:0,他引:3
X. H. Gong 《Journal of Optimization Theory and Applications》2007,133(2):151-161
In this paper, we introduce the concepts of globally efficient solution and cone-Benson efficient solution for a vector equilibrium
problem; we give some scalarization results for Henig efficient solution sets, globally efficient solution sets, weak efficient
solution sets, and cone-Benson efficient solution sets in locally convex spaces. Using the scalarization results, we show
the connectedness and path connectedness of weak efficient solution sets and various proper efficient solution sets of vector
equilibrium problem.
This research was partially supported by the National Natural Science Foundation of China and the Natural Science Foundation
of Jinxing Province, China. 相似文献
18.
研究了带约束条件集值优化问题近似Henig有效解集的连通性.在实局部凸Hausdorff空间中,讨论了可行域为弧连通紧的,目标函数为C-弧连通的条件下,带约束条件集值优化问题近似Henig有效解集的存在性和连通性.并给出了带约束条件集值优化问题近似Henig有效解集的连通性定理. 相似文献
19.
Truong Xuan Duc Ha 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(3):1305-1323
We present a new approach to the study of a set-valued equilibrium problem (for short, SEP) through the study of a set-valued optimization problem with a geometric constraint (for short, SOP) based on an equivalence between solutions of these problems. As illustrations, we adapt to SEP enhanced notions of relative Pareto efficient solutions introduced in set optimization by Bao and Mordukhovich and derive from known or new optimality conditions for various efficient solutions of SOP similar results for solutions of SEP as well as for solutions of a vector equilibrium problem and a vector variational inequality.We also introduce the concept of quasi weakly efficient solutions for the above problems and divide all efficient solutions under consideration into the Pareto-type group containing Pareto efficient, primary relative efficient, intrinsic relative efficient, quasi relative efficient solutions and the weak Pareto-type group containing quasi weakly efficient, weakly efficient, strongly efficient, positive properly efficient, Henig global properly efficient, Henig properly efficient, super efficient and Benson properly efficient solutions. The necessary conditions for Pareto-type efficient solutions and necessary/sufficient conditions for weak Pareto-type efficient solutions formulated here are expressed in terms of the Ioffe approximate coderivative and normal cone in the Banach space setting and in terms of the Mordukhovich coderivative and normal cone in the Asplund space setting. 相似文献
20.
基于已有的集值映射的弱次微分的概念,定义了集值映射的Henig全局次微分,研究了它的存在性条件以及运算性质.利用这一概念,分别给出了具约束向量集值最优化问题的Henig全局有效解对的必要性条件和充分性条件. 相似文献