In this paper we present two set-valued variants of the Ekeland variational principle involving the Clarke normal cone and establish sufficient conditions for a set-valued map to have a weak minimizer or a properly po...
详细信息
In this paper we present two set-valued variants of the Ekeland variational principle involving the Clarke normal cone and establish sufficient conditions for a set-valued map to have a weak minimizer or a properly positive minimizer when it satisfies Palais-Smale type conditions. (c) 2005 Elsevier Inc. All rights reserved.
Using variational analysis, we study vector optimization problems with objectives being closed multifunctions on Banach spaces or in Asplund spaces. In particular, in terms of the coderivatives, we present Fermat'...
详细信息
Using variational analysis, we study vector optimization problems with objectives being closed multifunctions on Banach spaces or in Asplund spaces. In particular, in terms of the coderivatives, we present Fermat's rules as necessary conditions for an optimal solution of the above problems. As applications, we also provide some necessary conditions (in terms of Clarke's normal cones or the limiting normal cones) for Pareto efficient points.
In this paper we use the Frechet, 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 p...
详细信息
In this paper we use the Frechet, 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. (C) 2003 Elsevier Inc. All rights reserved.
This paper introduces a kind of sub-Lipschitz continuity for set-valued mappings based on the cosmic metric. This type of Lipschitz behavior has applications with regards to necessary optimality conditions, the Hamilt...
详细信息
This paper introduces a kind of sub-Lipschitz continuity for set-valued mappings based on the cosmic metric. This type of Lipschitz behavior has applications with regards to necessary optimality conditions, the Hamilton-Jacobi equation, and invariance of unbounded differential inclusions. Cosmically Lipschitz assumptions allow for broader applications than previously allowed under Lipschitz assumptions. It is also shown that a cosmically Lipschitz mapping can be characterized by the normal cones to its graph using the coderivative, and various rules are presented in order to more easily identify such a mapping.
A condition ensuring calmness of a class of multifunctions between finite-dimensional spaces is derived in terms of subdifferential concepts developed by Mordukhovich. The considered class comprises general constraint...
详细信息
A condition ensuring calmness of a class of multifunctions between finite-dimensional spaces is derived in terms of subdifferential concepts developed by Mordukhovich. The considered class comprises general constraint set mappings as they occur in optimization or mappings associated with a certain type of variational system. The condition ensuring calmness is obtained as an appropriate reduction of Mordukhovich's well-known characterization of the stronger Aubin property. (Roughly spoken, one may pass to the boundaries of normal cones or subdifferentials when aiming at calmness.) It allows one to derive dual constraint qualifications in nonlinear optimization that are weaker than conventional ones (e.g., Mangasarian-Fromovitz) but still sufficient for the existence of Lagrange multipliers, (C) 2001 Academic Press.
The paper concerns an optimization problem with a generalized equation among the constraints. This model includes standard mathematical programs with parameter-dependent variational inequalities or complementarity pro...
详细信息
The paper concerns an optimization problem with a generalized equation among the constraints. This model includes standard mathematical programs with parameter-dependent variational inequalities or complementarity problems as side constraints. Using Mordukhovich's generalized differential calculus, we derive necessary optimality conditions and apply them to problems, where the equilibria are governed by implicit complementarity problems and by hemivariational inequalities.
An abstract subdifferential was employed to obtain a verifiable criterion for metric regularity of infinite dimensional multivalued mappings, satisfying the given convergence condition, and to study some important pro...
详细信息
An abstract subdifferential was employed to obtain a verifiable criterion for metric regularity of infinite dimensional multivalued mappings, satisfying the given convergence condition, and to study some important properties of multivalued mappings that are separately partially compactly epi-Lipschitzian. Some subclasses of partially compactly epi-Lipschitzian multivalued mappings were used to give necessary and sufficient conditions for metric regularity of infinite-dimensional multivalued mappings in finite dimensions. The metric regularity at (x0,y0) of a multivalued mapping F with F-1 uniformly compactly epi-Lipschitzian implies that the kernel of the approximate coderivative of F at (x0,y0) is reduced to zero.
We give a new necessary and sufficient condition for convexity of a set-valued map F between Banach spaces. It is established for a closed map F having nonconvex values. The main tool in this paper is the coderivative...
详细信息
We give a new necessary and sufficient condition for convexity of a set-valued map F between Banach spaces. It is established for a closed map F having nonconvex values. The main tool in this paper is the coderivative of F which is constructed with the help of an abstract subdifferential notion of Penot [16]. A detailed discussion is devoted to special cases when the contingent, the Frechet and the Clarke-Rockafellar subdifferentials are used as this abstract subdifferential.
We discuss three different characterizations of continuity properties for general multifunctions S : R-d double right arrow R-n. Each of these characterizations is given by the same simple nonsingularity condition, bu...
详细信息
We discuss three different characterizations of continuity properties for general multifunctions S : R-d double right arrow R-n. Each of these characterizations is given by the same simple nonsingularity condition, but stated in terms of three different generalized derivatives. Two of these characterizations are known, but the third is new to this paper. We discuss how all three have immediate analogues as generalized inverse mapping theorems, and we apply our new characterization to develop a fundamental and very broad sensitivity theorem for solutions to parameterized optimization problems.
We study the local surjectivity and openness properties of mappings and correspondences by using coderivatives. We recall local criteria but concentrate on point criteria. Our study relies on a compactness condition w...
详细信息
We study the local surjectivity and openness properties of mappings and correspondences by using coderivatives. We recall local criteria but concentrate on point criteria. Our study relies on a compactness condition which is of independent interest, for instance, for the study of the behavior of the injectivity constant of a linear map or of a convex process under stabilization procedures. Several known criteria for openness are shown to be a consequences of this new compactness condition. Mathematics Subject Classifications (1991): 26B05, 26B10, 26B25, 46G05, 49J52, 58C20.
暂无评论