Displaying similar documents to “Sufficient Second Order Optimality Conditions for C^1 Multiobjective Optimization Problems”

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...

Second-order optimality conditions for nondominated solutions of multiobjective programming with C 1 , 1 data

Liping Liu, Pekka Neittaanmäki, Michal Křížek (2000)

Applications of Mathematics

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We examine new second-order necessary conditions and sufficient conditions which characterize nondominated solutions of a generalized constrained multiobjective programming problem. The vector-valued criterion function as well as constraint functions are supposed to be from the class C 1 , 1 . Second-order optimality conditions for local Pareto solutions are derived as a special case.

On constraint qualifications in directionally differentiable multiobjective optimization problems

Giorgio Giorgi, Bienvenido Jiménez, Vincente Novo (2010)

RAIRO - Operations Research

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We consider a multiobjective optimization problem with a feasible set defined by inequality and equality constraints such that all functions are, at least, Dini differentiable (in some cases, Hadamard differentiable and sometimes, quasiconvex). Several constraint qualifications are given in such a way that generalize both the qualifications introduced by Maeda and the classical ones, when the functions are differentiable. The relationships between them are analyzed. Finally, we give...

LFS functions in multi-objective programming

Luka Neralić, Sanjo Zlobec (1996)

Applications of Mathematics

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We find conditions, in multi-objective convex programming with nonsmooth functions, when the sets of efficient (Pareto) and properly efficient solutions coincide. This occurs, in particular, when all functions have locally flat surfaces (LFS). In the absence of the LFS property the two sets are generally different and the characterizations of efficient solutions assume an asymptotic form for problems with three or more variables. The results are applied to a problem in highway construction,...