共查询到20条相似文献,搜索用时 15 毫秒
1.
Luis Rodríguez-Marín Miguel Sama 《Nonlinear Analysis: Theory, Methods & Applications》2008,68(12):3780-3788
In this paper we introduce a notion of the τw-contingent epiderivative of a set-valued map by considering the weak topology in the image space. We establish a chain rule formula for families of τw-contingent and contingent epiderivatives. When the image space is reflexive and the ordering cone a half-space, we give conditions for the existence of the family of τw-contingent epiderivatives of a stable set-valued map; moreover we obtain an interesting formula that connects this family with the contingent epiderivative of an associated scalar set-valued map. Finally we apply the previous results in order to establish optimality conditions for a set-valued optimization problem via epiderivatives with respect to half-spaces associated with the ordering cone. In particular we provide a scalarization method for computing these conditions in reflexive spaces. 相似文献
2.
This short note deals with the issue of existence of contingent epiderivatives for set-valued maps defined from a real normed space to the real line. A theorem of Jahn-Rauh [1], given for the existence of contingent epiderivatives, is used to obtain more general existence results. The strength and the limitations of the main result are discussed by means of some examples. 相似文献
3.
Bienvenido Jiménez Miguel Sama 《Journal of Mathematical Analysis and Applications》2009,352(2):788-2157
In this paper necessary and sufficient conditions for strict minimizers of a general vector optimization problem are given by means of different notions of graphical or epigraphical derivatives, extending some existing results in the literature. In first place, these conditions are established by means of contingent derivatives and secondly, by applying a nonconvex separation result, in terms of contingent epiderivatives and hypoderivatives. Moreover, through a variational approach, a scalarization method is developed in order to obtain scalar versions of these results. 相似文献
4.
Luis Rodríguez-Marín 《Journal of Mathematical Analysis and Applications》2007,335(2):1374-1382
In this paper the existence of the contingent epiderivative of a set-valued map is studied from a variational perspective. We give a variational characterization of the ideal minimal of a weakly compact set. As a consequence we characterize the existence of the contingent epiderivative in terms of an associated family of variational systems. When a set-valued map takes values in Rn we show that these systems can be formulated in terms of the contingent epiderivatives of scalar set-valued maps. By applying these results we extend some existing theorems. 相似文献
5.
P. Jiménez Guerra M.A. Melguizo 《Journal of Mathematical Analysis and Applications》2010,372(1):197-207
The aim of this paper is to formulate an envelope theorem for vector convex programs. The obtained result allows to quantify the changes of a certain set of optimal values according to changes of any of the parameters which appear in the constraints. We show that the sensitivity depends on a set of associated Lagrange multipliers and its sensitivity. 相似文献
6.
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
7.
D.E. Ward 《Journal of Mathematical Analysis and Applications》2008,348(1):324-336
A chain rule is established for contingent and adjacent epiderivatives and hypoderivatives of compositions g○h, where h is assumed to be Hadamard directionally differentiable. Corollaries include a formula for the contingent and adjacent cones of an equality constraint set defined by a Hadamard directionally differentiable function. An analogous chain rule for second-order contingent and adjacent epiderivatives and hypoderivatives is also developed. 相似文献
8.
This paper deals with the set-valued vector quasiequilibrium problem of finding a point (z
0,x
0) of a set E×K such that (z
0,x
0)∈B(z
0,x
0)×A(z
0,x
0), and, for all η∈A(z
0,x
0),
where α is a subset of 2
Y
×2
Y
and A:E×K→2
K
,B:E×K→2
E
,F:E×K×K→2
Y
, C:E×K×K→2
Y
are set-valued maps, with Y is a topological vector space. Two existence theorems are proven under different assumptions. Correct results of [Hou, S.H.,
Yu, H., Chen, G.Y.: J. Optim. Theory Appl. 119, 485–498 (2003)] are obtained from a special case of one of these theorems.
The authors are indebted to the referees for valuable remarks. 相似文献
9.
《Optimization》2012,61(4):771-797
In this paper, we consider extended vector-valued mappings defined on a normed linear space. Based on the recent semicontinuous regularizations related to hypographical and/or epigraphical profile mappings of the considered function introduced, we define semicontinuous radial epiderivatives. We, then, demonstrate that the properties of these epiderivatives amount to properties of hypographical and/or epigraphical profile mappings of the corresponding difference quotient of the underlying function, which simplify fairly well the proofs in the radial epiderivative formulaes. In particular, we stress the impact of semicontinuity, hence, we characterize with new arguments the radial epiderivatives in terms of the suprema and/or infima of the interiorly radial cone of the hypograph and/or epigraph of the considered function. Finally, we obtain optimality conditions for general non-convex constrained vector optimization problems. We apply thereafter the obtained pattern to a parametric quasiconvex programming problem for which we derive necessary and sufficient optimality conditions that are not sensitive to perturbation at the nominal level, yielding henceforth more – and strong at least under asymptotically regular constraints – information than the recent stability results obtained under additional conditions on the regularity of the normal cone to the adjusted sublevel sets of the underlying function. 相似文献
10.
Generalized Constraint Qualifications and Optimality Conditions for Set-Valued Optimization Problems
Huang Yong-Wei 《Journal of Mathematical Analysis and Applications》2002,265(2):309-321
In this paper we discuss the connections of four generalized constraint qualifications for set-valued vector optimization problems with constraints. Then some K-T type necessary and sufficient optimality conditions are derived, in terms of the contingent epiderivatives. 相似文献
11.
Ben Liu 《Numerical Functional Analysis & Optimization》2013,34(1):50-67
In this article, we introduce a second-order modified contingent cone and a second-order modified contingent epiderivative. We discuss some properties of the second-order cone and the epiderivative, respectively. Moreover, a Fritz John type necessary optimality condition is obtained for the set-valued optimization problems with constraints by using the second-order modified contingent epiderivative and an example is proposed to explain the Fritz John type necessary optimality condition. In particular, we obtain a unified second-order sufficient and necessary optimality condition for the set-valued optimization problems with constraints under twice differentiable L-quasi-convex assumption. 相似文献
12.
Luis Rodríguez-Marín 《Journal of Mathematical Analysis and Applications》2008,342(1):371-385
This article deals with derivatives for set-valued maps that take values in ordered vector spaces, in particular it concerns about the relationship between the epiderivatives of a set-valued map and its associated map of infima. When the image space is a real separable Hilbert space ordered by an orthonormal basis, by using a variational technique based on a decoupling of the ordering cone into half-spaces, we show that both epiderivatives coincide under certain hypothesis of compactness and stability. Furthermore we obtain some computation formulas for these derivatives in terms of associated scalar set-valued maps. 相似文献
13.
F. García M.A. Melguizo Padial M.J. Muñoz-Bouzo 《Journal of Mathematical Analysis and Applications》2015
The aim of this note is to formulate an envelope theorem for vector convex programs. This version corrects an earlier work, “The envelope theorem for multiobjective convex programming via contingent derivatives” by Jiménez Guerra et al. (2010) [3]. We first propose a necessary and sufficient condition allowing to restate the main result proved in the alluded paper. Second, we introduce a new Lagrange multiplier in order to obtain an envelope theorem avoiding the aforementioned error. 相似文献
14.
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
15.
M. Durea 《Journal of Optimization Theory and Applications》2007,133(1):111-116
In this note, we derive first and second-order necessary (resp. sufficient) conditions for local minimum (resp. strict local
minimum) points of optimization problems governed by set-valued maps. This allows us to present and to solve a generalized
Lagrange claim in a multivalued setting. 相似文献
16.
非凸向量集值优化Benson真有效解的最优性条件与对偶 总被引:7,自引:0,他引:7
在无需偏序锥内部非空的情况下给出了非凸约束向量集值优化Benaon真有效解一种加细的最优性条件,并建立了向量集值优化Benson真有效解一种改进的Lagrange乘子型对偶,它比已有的Lagrange乘子型对偶具有较好的对偶性。 相似文献
17.
CONE-DIRECTED CONTINGENT DERIVATIVES AND GENERALIZED PREINVEX SET-VALUED OPTIMIZATION 总被引:2,自引:0,他引:2
丘京辉 《数学物理学报(B辑英文版)》2007,27(1):211-218
By using cone-directed contingent derivatives, the unified necessary and suffi-cient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set valued optimization. 相似文献
18.
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
19.
Miguel Sama 《Journal of Mathematical Analysis and Applications》2010,372(1):262-272
This paper underlines the role of directional compactness in the scalarization of graphical derivatives of set-valued maps taking values in infinite-dimensional spaces. Two main theorems are given. The first one states the equivalence of contingent epiderivatives and τw-contingent epiderivatives for directionally compact maps. The second main result proves a variational characterization for the contingent epiderivative of stable and directionally compact maps taking values in general image spaces, extending known results in finite-dimensional and reflexive Banach spaces. The hypotheses given are minimal as is shown by means of several examples. Connections of these theorems with other results of the literature are also provided. 相似文献
20.
锥凸集值映射的基本性质 总被引:3,自引:0,他引:3
本文首先在R~m的幂集上定义了一种锥序关系并借助这种序关系定义锥凸集值映射,证明了普通单值凸函数的一些基本性质拓广到这种锥凸集值映射时仍成立. 相似文献