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1.
集值映射的广义梯度和全局真有效解 总被引:1,自引:1,他引:0
本文利用集值映射的上图导数引进了全局真有效意义下的广义梯度和广义次微分的概念,并且给出了集值映射全局真有效次微分的存在定理,还建立了集值向量优化问题全局真有效解在次微分形式下的最优性条件. 相似文献
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集值优化问题的Benson真有效解的广义导数型最优性条件 总被引:6,自引:0,他引:6
引进了集值映射关于锥的Clarke切导数, Adjacent切导数与Contingent切导数概念;应用它们导出了具Slater约束规格的集值优化问题的Benson真有效解的广义导数型最优性条件. 相似文献
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在本文里,集值映射的Epi-导数被引入,它可以认作是实值Lipschitz函数的Clarke-广义方向导数的推广,同时它的一些性质也被研究.进一步地,利用这个Epi-导数集值映射的次微分被定义并研究它的性质.作为其应用,我们给出了集值优化问题的一些(必要或充分)最优性条件. 相似文献
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讨论拓扑向量空间中无约束集值优化问题的最优性条件问题.利用集值映射的Dini方向导数,在广义锥-预不变凸性条件下,建立了集值优化问题关于弱极小元和强极小元的最优性充分必要条件. 相似文献
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引进了集值映射关于锥的(1,α)-阶Clarke切导数,(1,α)-阶Adjacent切导数,(1,α)-阶Contingent切导数概念;应用它们导出了具Slater约束规格的集值优化问题的Benson真有效解的广义Kuhn-Tucker最优性条件. 相似文献
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文中用一般集值映射定义了向量函数和集值映射的广义ε-共轭映射和ε-次分微分,讨论了它们之间的关系,以此为基础,建立了集值映射最优化问题的ε-共轭对偶定理。 相似文献
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广义次似凸集值优化的鞍点定理 总被引:1,自引:1,他引:0
周志昂 《数学的实践与认识》2007,37(13):139-143
讨论广义次似凸集值优化的鞍点定理.给出广义次似凸集值映射的两个性质.定义广义次似凸集值优化的Fritz-John鞍点和Kuhn-Tucker鞍点.获得一系列广义次似凸集值优化的鞍点定理. 相似文献
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In this paper, some exact calculus rules are obtained for calculating the coderivatives of the composition of two multivalued
maps. Similar rules are displayed for sums. A crucial role is played by an intermediate set-valued map called the resolvent.
We first establish inclusions for contingent, Fréchet and limiting coderivatives. Combining them, we get equality rules. The
qualification conditions we present are natural and less exacting than classical conditions. 相似文献
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《Optimization》2012,61(7):1075-1098
The aim of this article is to investigate codifferential properties of a class of set-valued maps and gap function involving vector variational inequality. Relationships between their coderivatives are discussed. Formulae for computing coderivatives of the gap function are established. Optimality conditions of solutions for vector variational inequalities are obtained. The finite-dimensional cases are also discussed. 相似文献
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研究了广义微分结构中的集合方向Mordukhovich法锥、集值映射的方向上导数,以及集合和集值映射的方向序列法紧性的分析法则. 基于集合方向Mordukhovich法锥的交集法则,在方向内半紧性假设下,建立了集合的方向Mordukhovich法锥、集值映射的方向上导数的分析法则.此外,借助Asplund乘积空间中集合的方向序列法紧性的交集法则, 在方向内半紧性和相应的规范条件下,建立了集合和集值映射的(部分)方向序列法紧性的加法、逆像、复合等法则. 相似文献
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In this paper, we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic results of convex subdifferential calculus in full generality and also derive new results of convex analysis concerning optimal value/marginal functions, normals to inverse images of sets under set-valued mappings, calculus rules for coderivatives of single-valued and set-valued mappings, and calculating coderivatives of solution maps to parameterized generalized equations governed by set-valued mappings with convex graphs. 相似文献
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本文利用集值映射弱次梯度的Morea-Rockafellar定理,在内部(锥)-凸性假设下,得到了集值映射关于Henig有效性的Morea-Rockafellar定理.其结论为:在内部(锥)-凸条件下,两个集值映射和的Henig有效次梯度可以表示成它们Henig有效次梯度的和. 相似文献
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Li-Ping Pang Fan-Yun Meng Jian Lv Qi Tian 《Numerical Functional Analysis & Optimization》2018,39(2):155-178
This paper mainly establishes the sensitivity analysis of a multiobjective optimization problem with parameterized quasi-variational inequalities (QVIs). Using the (regular) coderivative of the associated epigraphical multifunction, the (regular) subdifferentials of the efficient frontier maps are estimated, which involve the (regular) coderivatives of the solution mapping to the parameterized QVIs. Under the linear independent constraint qualification, the defined auxiliary set-valued mappings in the parameterized QVIs are clam. The detailed formulae of subdifferentials of the efficient frontier maps are obtained and examples are simultaneously provided for analyzing and illustrating the obtained results. 相似文献
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In this work we study the directional versions of Mordukhovich normal cones to nonsmooth sets, coderivatives of set-valued mappings, and subdifferentials of extended-real-valued functions in the framework of general Banach spaces. We establish some characterizations and basic properties of these constructions, and then develop calculus including sum rules and chain rules involving smooth functions. As an application, we also explore the upper estimates of the directional Mordukhovich subdifferentials and singular subdifferentials of marginal functions. 相似文献
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Truong Xuan Duc Ha 《Journal of Mathematical Analysis and Applications》2005,311(2):647-663
In this paper we investigate a vector optimization problem (P) where objective and constraints are given by set-valued maps. We show that by mean of marginal functions and suitable scalarizing functions one can characterize certain solutions of (P) as solutions of a scalar optimization problem (SP) with single-valued objective and constraint functions. Then applying some classical or recent results in optimization theory to (SP) and using estimates of subdifferentials of marginal functions, we obtain optimality conditions for (P) expressed in terms of Lagrange or sequential Lagrange multipliers associated with various coderivatives of the set-valued data. 相似文献
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Truong Xuan Duc Ha 《Journal of Mathematical Analysis and Applications》2003,286(2):509-523
In this paper we use the Fréchet, Clarke, and Mordukhovich coderivatives to obtain variants of the Ekeland variational principle for a set-valued map F and establish optimality conditions for set-valued optimization problems. Our technique is based on scalarization with the help of a marginal function associated with F and estimates of subdifferentials of this function in terms of coderivatives of F. 相似文献
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P. H. Sach 《Journal of Optimization Theory and Applications》2007,133(2):213-227
In this paper, we introduce the notion of (Benson) proper subgradient of a set-valued map and prove that, for some class of
nonconvex set-valued maps, a proper subgradient of the sum of two set-valued maps can be expressed as the sum of two proper
subgradients of these maps. This property is also established for weak subgradients. A result in Ref. [Lin, L.J.: J. Math.
Anal. Appl. 186, 30–51 (1994)], obtained under some convexity assumption, is included as a special case of the corresponding result of this paper.
The author thanks the anonymous referees for their valuable remarks. 相似文献