### Weak $\psi $-sharp minima in vector optimization problems.

Xu, S., Li, S.J. (2010)

Fixed Point Theory and Applications [electronic only]

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Xu, S., Li, S.J. (2010)

Fixed Point Theory and Applications [electronic only]

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Ewa Bednarczuk (2007)

Control and Cybernetics

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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).

Aboussoror, Abdelmalek, Loridan, Pierre (1995)

Serdica Mathematical Journal

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We are concerned with two-level optimization problems called strongweak Stackelberg problems, generalizing the class of Stackelberg problems in the strong and weak sense. In order to handle the fact that the considered two-level optimization problems may fail to have a solution under mild assumptions, we consider a regularization involving ε-approximate optimal solutions in the lower level problems. We prove the existence of optimal solutions for such regularized problems and present...

Durea, M. (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 46A30, 54C60, 90C26. In this paper we prove two results of nonsmooth analysis involving the Fréchet subdifferential. One of these results provides a necessary optimality condition for an optimization problem which arise naturally from a class of wide studied problems. In the second result we establish a sufficient condition for the metric regularity of a set-valued map without continuity assumptions.

Truong Q. Bao, Boris S. Mordukhovich (2007)

Applications of Mathematics

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In this paper we study set-valued optimization problems with equilibrium constraints (SOPECs) described by parametric generalized equations in the form $$0\in G\left(x\right)+Q\left(x\right),$$ where both $G$ and $Q$ are set-valued mappings between infinite-dimensional spaces. Such models particularly arise from certain optimization-related problems governed by set-valued variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish general results on the existence of optimal solutions...

Giancarlo Bigi, Marco Castellani (2010)

RAIRO - Operations Research

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A second order optimality condition for multiobjective optimization with a set constraint is developed; this condition is expressed as the impossibility of nonhomogeneous linear systems. When the constraint is given in terms of inequalities and equalities, it can be turned into a John type multipliers rule, using a nonhomogeneous Motzkin Theorem of the Alternative. Adding weak second order regularity assumptions, Karush, Kuhn-Tucker type conditions are therefore deduced. ...