Displaying similar documents to “On constraint qualifications in directionally differentiable multiobjective optimization problems”

On constraint qualifications in directionally differentiable multiobjective optimization problems

Giorgio Giorgi, Bienvenido Jiménez, Vincente Novo (2004)

RAIRO - Operations Research - Recherche Opérationnelle

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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...

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).

Second order optimality conditions for differentiable multiobjective problems

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. ...

On dual vector optimization and shadow prices

Letizia Pellegrini (2010)

RAIRO - Operations Research

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In this paper we present the image space analysis, based on a general separation scheme, with the aim of studying Lagrangian duality and shadow prices in Vector Optimization. Two particular kinds of separation are considered; in the linear case, each of them is applied to the study of sensitivity analysis, and it is proved that the derivatives of the perturbation function can be expressed in terms of vector Lagrange multipliers or shadow prices.