Displaying similar documents to “ ε -duality theorems for convex semidefinite optimization problems with conic constraints.”

Strict minimizers of order m in nonsmooth optimization problems

Tadeusz Antczak, Krzysztof Kisiel (2006)

Commentationes Mathematicae Universitatis Carolinae

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In the paper, some sufficient optimality conditions for strict minima of order m in constrained nonlinear mathematical programming problems involving (locally Lipschitz) ( F , ρ ) -convex functions of order m are presented. Furthermore, the concept of strict local minimizer of order m is also used to state various duality results in the sense of Mond-Weir and in the sense of Wolfe for such nondifferentiable optimization problems.

Optimality conditions for weak efficiency to vector optimization problems with composed convex functions

Radu Boţ, Ioan Hodrea, Gert Wanka (2008)

Open Mathematics

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We consider a convex optimization problem with a vector valued function as objective function and convex cone inequality constraints. We suppose that each entry of the objective function is the composition of some convex functions. Our aim is to provide necessary and sufficient conditions for the weakly efficient solutions of this vector problem. Moreover, a multiobjective dual treatment is given and weak and strong duality assertions are proved.