Displaying similar documents to “Existence of minimizers and necessary conditions in set-valued optimization with equilibrium constraints”

Optimality conditions for a class of mathematical programs with equilibrium constraints: strongly regular case

Jiří V. Outrata (1999)

Kybernetika

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The paper deals with mathematical programs, where parameter-dependent nonlinear complementarity problems arise as side constraints. Using the generalized differential calculus for nonsmooth and set-valued mappings due to B. Mordukhovich, we compute the so-called coderivative of the map assigning the parameter the (set of) solutions to the respective complementarity problem. This enables, in particular, to derive useful 1st-order necessary optimality conditions, provided the complementarity...

Sufficient Second Order Optimality Conditions for C^1 Multiobjective Optimization Problems

Gadhi, N. (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 90C29; Secondary 90C30. In this work, we use the notion of Approximate Hessian introduced by Jeyakumar and Luc [19], and a special scalarization to establish sufficient optimality conditions for constrained multiobjective optimization problems. Throughout this paper, the data are assumed to be of class C^1, but not necessarily of class C^(1.1).

On necessary optimality conditions in a class of optimization problems

Jiří V. Outrata (1989)

Aplikace matematiky

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In the paper necessary optimality conditions are derived for the minimization of a locally Lipschitz objective with respect to the consttraints x ∈ S , 0 ∈ F ( x ) , where S is a closed set and F is a set-valued map. No convexity requirements are imposed on F . The conditions are applied to a generalized mathematical programming problem and to an abstract finite-dimensional optimal control problem.