共查询到20条相似文献,搜索用时 11 毫秒
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In this paper, a family of parameterized set-valued optimization problems, whose constraint set depends on a parameter, are considered. Some calculus rules are obtained for calculating the second-order contingent derivatives of the composition and sum of two set-valued mappings. Then, by using these calculus rules, some results concerning second-order sensitivity analysis are established, and an explicit expression for the second-order contingent derivative of the (weak) perturbation mapping in the set-valued optimization problems is obtained. 相似文献
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Akhtar A. Khan 《Optimization》2013,62(6):743-758
In this article we give new second-order optimality conditions in set-valued optimization. We use the second-order asymptotic tangent cones to define second-order asymptotic derivatives and employ them to give the optimality conditions. We extend the well-known Dubovitskii–Milutin approach to set-valued optimization to express the optimality conditions given as an empty intersection of certain cones in the objective space. We also use some duality arguments to give new multiplier rules. By following the more commonly adopted direct approach, we also give optimality conditions in terms of a disjunction of certain cones in the image space. Several particular cases are discussed. 相似文献
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Giovanni P. Crespi Ivan Ginchev Matteo Rocca 《Mathematical Methods of Operations Research》2006,63(1):87-106
A a set-valued optimization problem min
C
F(x), x ∈X
0, is considered, where X
0 ⊂ X, X and Y are normed spaces, F: X
0 ⊂ Y is a set-valued function and C ⊂ Y is a closed cone. The solutions of the set-valued problem are defined as pairs (x
0,y
0), y
0 ∈F(x
0), and are called minimizers. The notions of w-minimizers (weakly efficient points), p-minimizers (properly efficient points) and i-minimizers (isolated minimizers) are introduced and characterized through the so called oriented distance. The relation between
p-minimizers and i-minimizers under Lipschitz type conditions is investigated. The main purpose of the paper is to derive in terms of the Dini
directional derivative first order necessary conditions and sufficient conditions a pair (x
0, y
0) to be a w-minimizer, and similarly to be a i-minimizer. The i-minimizers seem to be a new concept in set-valued optimization. For the case of w-minimizers some comparison with existing results is done. 相似文献
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Contingent epiderivatives and set-valued optimization 总被引:24,自引:0,他引:24
In this paper we introduce the concept of the contingent epiderivative for a set-valued map which modifies a notion introduced by Aubin [2] as upper contingent derivative. It is shown that this kind of a derivative has important properties and is one possible generalization of directional derivatives in the single-valued convex case. For optimization problems with a set-valued objective function optimality conditions based on the concept of the contingent epiderivative are proved which are necessary and sufficient under suitable assumptions. 相似文献
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Guo-lin Yu 《高校应用数学学报(英文版)》2017,32(2):225-236
There are two approaches of defining the solutions of a set-valued optimization problem:vector criterion and set criterion.This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives.In the case of vector criterion,some optimality conditions are derived for isolated (weak) minimizers.With set criterion,necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation. 相似文献
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Truong Xuan Duc Ha 《Optimization》2018,67(7):1031-1050
AbstractIn this paper, we follow Kuroiwa’s set approach in set optimization, which proposes to compare values of a set-valued objective map F with respect to various set order relations. We introduce a Hausdorff-type distance relative to an ordering cone between two sets in a Banach space and use it to define a directional derivative for F. We show that the distance has nice properties regarding set order relations and the directional derivative enjoys most properties of the one of a scalar single-valued function. These properties allow us to derive necessary and/or sufficient conditions for various types of maximizers and minimizers of F. 相似文献
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In this paper, higher order generalized contingent epiderivative and higher order generalized adjacent epiderivative of set-valued maps are introduced. Necessary and sufficient conditions for Henig efficient solutions to a constrained set-valued optimization problem are given by employing the higher order generalized epiderivatives. 相似文献
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给出实的赋范空间中集值映射的Henig真有效解集的一些性质,并利用集值映射的相依上图导数和集值映射的次微分给出了集值优化问题Henig真有效解的最优性条件的充要条件. 相似文献
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Optimality conditions in non-convex set-valued optimization 总被引:2,自引:0,他引:2
Fabián Flores-Bazán 《Mathematical Methods of Operations Research》2001,53(3):403-417
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本文引入了集值映射的锥方向的高阶广义邻近导数.应用这种导数,构建了约束的集值优化问题的一种高阶Mond-Weir型对偶,并建立了相应的弱对偶,强对偶和逆对偶性,获得的结果推广了文献中的相应结论. 相似文献
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《Optimization》2012,61(3):449-471
We study a nonsmooth vector optimization problem with an arbitrary feasible set or a feasible set defined by a generalized inequality constraint and an equality constraint. We assume that the involved functions are nondifferentiable. First, we provide some calculus rules for the contingent derivative in which the stability (a local Lipschitz property at a point) of the functions plays a crucial role. Second, another calculus rules are established for steady functions. Third, necessary optimality conditions are stated using tangent cones to the feasible set and the contingent derivative of the objective function. Finally, some necessary and sufficient conditions are presented through Lagrange multiplier rules. 相似文献
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Directional derivatives in nonsmooth optimization 总被引:2,自引:0,他引:2
In this note, we consider two notions of second-order directional derivatives and discuss their use in the characterization of minimal points for nonsmooth functions.This research was supported by NSF Grant No. ECS-8214081, by the Fund for Promotion of Research at the Technion, and by Deutsche Forschungsgemeinschaft. 相似文献
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Problems in set-valued optimization can be solved via set optimization. In this paper optimality conditions are studied for set-valued maps with set optimization. Optimality requirements are established for continuous selections using directional derivatives. Necessary and sufficient conditions for the existence of solutions are shown for set-valued maps under generalized convexity assumptions and with the notion of the contingent derivative. 相似文献
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Positivity - In the paper, we develop sum and chain rules of the generalized contingent derivative for set-valued mappings. Then, their applications to sensitivity analysis and optimality... 相似文献
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In this paper we introduce several concepts of approximate solutions of set-valued optimization problems with vector and set optimization. We prove existence results and necessary and sufficient conditions by using limit sets. 相似文献
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本文在集值优化的框架下提出了一个二层多目标规划模型(BLMOP).利用集值映射的相依导数和相依上导数,给出了几个有关(BLMOP)的弱有效解的必要或充分最优性条件. 相似文献
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超有效意义下向量集值优化修整的Lagrange乘子型对偶 总被引:2,自引:0,他引:2
给出了一类加细的向量集值优化超有效解的最优性条件,由此给出了一种改进的Lagrange乘子型对偶,并建立了对偶的弱定理,正定理及逆定理。 相似文献