In this paper, we study the mordukhovich coderivative and the local metric regularity in Robinson's sense of the solution map to a parametric dynamic programming problem with linear constraints and convex cost fun...
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In this paper, we study the mordukhovich coderivative and the local metric regularity in Robinson's sense of the solution map to a parametric dynamic programming problem with linear constraints and convex cost functions. By establishing abstract results on the coderivative and the local metric regularity of the solution map to a parametric variational inequality, we obtain the mordukhovich coderivative and the local metric regularity in Robinson's sense of the solution map to a parametric discrete optimal control problem.
We study the global homeomorphism of a continuous nonsmooth mappings between Riemannian manifolds which may be non-locally Lipschitz. To this end, we use the notion of pseudo-Jacobian map associated to f:M -> N whe...
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We study the global homeomorphism of a continuous nonsmooth mappings between Riemannian manifolds which may be non-locally Lipschitz. To this end, we use the notion of pseudo-Jacobian map associated to f:M -> N where M and N are Riemannian manifolds and we consider a related index of regularity for f. We obtain a characterization of global homeomorphisms in terms of its index of regularity.
This paper deals with the Frechet and mordukhovich coderivatives of the normal cone mapping related to the parametric extended trust region subproblems (eTRS), in which the trust region intersects a ball with a single...
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This paper deals with the Frechet and mordukhovich coderivatives of the normal cone mapping related to the parametric extended trust region subproblems (eTRS), in which the trust region intersects a ball with a single linear inequality constraint. We use the obtained results to investigate the Lipschitzian stability of parametric eTRS. We also propose a necessary condition for the local (or global) solution of the eTRS by using the coderivative tool.
The purpose of this paper is to consider the set-valued optimization problem in Asplund spaces without convexity assumption. By a scalarization function introduced by Tammer and Weidner (J Optim Theory Appl 67:297-320...
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The purpose of this paper is to consider the set-valued optimization problem in Asplund spaces without convexity assumption. By a scalarization function introduced by Tammer and Weidner (J Optim Theory Appl 67:297-320, 1990), we obtain the Lagrangian condition for approximate solutions on set-valued optimization problems in terms of the mordukhovich coderivative.
In this paper, without using any regularity assumptions, we derive a new exact formula for computing the Fr,chet coderivative and an exact formula for the mordukhovich coderivative of normal cone mappings to perturbed...
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In this paper, without using any regularity assumptions, we derive a new exact formula for computing the Fr,chet coderivative and an exact formula for the mordukhovich coderivative of normal cone mappings to perturbed polyhedral convex sets. Our development establishes generalizations and complements of the existing results on the topic. An example to illustrate formulae is given.
This paper establishes an upper estimate for the Fr,chet normal cone to the graph of the nonlinearly perturbed polyhedral normal cone mappings in finite dimensional spaces. Under a positive linear independence assumpt...
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This paper establishes an upper estimate for the Fr,chet normal cone to the graph of the nonlinearly perturbed polyhedral normal cone mappings in finite dimensional spaces. Under a positive linear independence assumption on the normal vectors of the active constraints at the point in question, the result leads to an upper estimate for values of the mordukhovich coderivative of such mappings. On the basis, new results on solution stability of parametric affine variational inequalities under nonlinear perturbations are derived.
Under a mild regularity assumption, we derive an exact formula for the Frechet coderivative and some estimates for the mordukhovich coderivative of the normal cone mappings of perturbed polyhedra in reflexive Banach s...
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Under a mild regularity assumption, we derive an exact formula for the Frechet coderivative and some estimates for the mordukhovich coderivative of the normal cone mappings of perturbed polyhedra in reflexive Banach spaces. Our focus point is a positive linear independence condition, which is a relaxed form of the linear independence condition employed recently by Henrion et al. (2010) [1], and Nam (2010) [3]. The formulae obtained allow us to get new results on solution stability of affine variational inequalities under linear perturbations. Thus, our paper develops some aspects of the work of Henrion et al. (2010) [1] Nam (2010) [3] Qui (in press) [12] and Yao and Yen (2009) [6,7]. (C) 2010 Elsevier Ltd. All rights reserved.
The aim of this article is to obtain necessary optimality conditions for Pareto minima in set-valued optimization problems. We employ a new method to derive generalized Fermat rules for set-valued optimization. This m...
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The aim of this article is to obtain necessary optimality conditions for Pareto minima in set-valued optimization problems. We employ a new method to derive generalized Fermat rules for set-valued optimization. This method is based on openness results for multifunctions and allows recovery of a large number of results and, at the same time, getting several new ones.
This paper establishes an exact formula for the Frechet coderivative and some estimates for the mordukhovich coderivative of the linearly perturbed normal cone mappings in reflexive Banach spaces. In comparison with N...
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This paper establishes an exact formula for the Frechet coderivative and some estimates for the mordukhovich coderivative of the linearly perturbed normal cone mappings in reflexive Banach spaces. In comparison with Nam (2010) [5], Qui (in press) [8], Qui (2011) [7], Trang (2010) [9]. the major advantage of our investigation is that here neither the linear independence condition nor the positively linear independence condition are used. Thus, no assumption on the normal vectors of the active constraints at the point in question is needed. Some aspects of the preceding results (Henrion, mordukhovich and Nam (2010) [3], Nam (2009) [5], Qui (2011) [7], Yao and Yen (2009) [10], Yao and Yen (2009) [11]) are developed. (C) 2011 Elsevier Inc. All rights reserved.
The paper deals with co-derivative formulae for normal cone mappings to smooth inequality systems. Both the regular (Linear Independence Constraint Qualification satisfied) and nonregular (Mangasarian-Fromovitz Constr...
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The paper deals with co-derivative formulae for normal cone mappings to smooth inequality systems. Both the regular (Linear Independence Constraint Qualification satisfied) and nonregular (Mangasarian-Fromovitz Constraint Qualification satisfied) cases are considered. A major part of the results relies on general transformation formulae previously obtained by mordukhovich and Outrata. This allows one to derive exact formulae for general smooth, regular and polyhedral, possibly nonregular systems. In the nonregular, nonpolyhedral case a generalized transformation formula by mordukhovich and Outrata applies, however, a major difficulty consists in checking a calmness condition of a certain multivalued mapping. The paper provides a translation of this condition in terms of much easier to verify constraint qualifications. The final section is devoted to the situation where the calmness condition is violated. A series of examples illustrates the use and comparison of the presented formulae. (C) 2008 Elsevier Ltd. All rights reserved.
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