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Saddle point criteria for second order η -approximated vector optimization problems

Anurag Jayswal, Shalini Jha, Sarita Choudhury (2016)

Kybernetika

The purpose of this paper is to apply second order η -approximation method introduced to optimization theory by Antczak [2] to obtain a new second order η -saddle point criteria for vector optimization problems involving second order invex functions. Therefore, a second order η -saddle point and the second order η -Lagrange function are defined for the second order η -approximated vector optimization problem constructed in this approach. Then, the equivalence between an (weak) efficient solution of the...

Second order optimality conditions for differentiable multiobjective problems

Giancarlo Bigi, Marco Castellani (2010)

RAIRO - Operations Research

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.

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

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.

Separation of convex polyhedral sets with column parameters

Milan Hladík (2008)

Kybernetika

Separation is a famous principle and separation properties are important for optimization theory and various applications. In practice, input data are rarely known exactly and it is advisable to deal with parameters. In this article, we are concerned with the basic characteristics (existence, description, stability etc.) of separating hyperplanes of two convex polyhedral sets depending on parameters. We study the case, when parameters are situated in one column of the constraint matrix from the...

Sobre soluciones óptimas en problemas de optimización multiobjetivo.

David Ríos Insua (1987)

Trabajos de Investigación Operativa

Estudiamos los principales tipos de conceptos de óptimo considerados en problemas de optimización multiobjetivo, cuando la ordenación de alternativas se regula mediante un cono K convexo: soluciones K-maximales, débilmente K-maximales, fuertemente K-maximales, propiamente K-maximales. Damos caracterizaciones en problemas generales de optimización vectorial y condiciones suficientes en problemas de maximización de funciones de valor vectoriales y escalares, particularizando después al caso de conos...

Soluciones propias en la teoría de la dominación.

Luis Coladas Uría (1983)

Trabajos de Estadística e Investigación Operativa

Se relacionan varios conceptos de "punto propiamente no dominado", introducidos para eliminar soluciones no dominadas "poco deseables", dándose condiciones para las distintas implicaciones y equivalencias.

Solution approaches to large shift scheduling problems

Monia Rekik, Jean-François Cordeau, François Soumis (2008)

RAIRO - Operations Research

This paper considers large shift scheduling problems with different shift start times and lengths, fractionable breaks and work stretch duration restrictions. Two solution approaches are proposed to solve the problems over a multiple-day planning horizon. The first approach is based on a local branching strategy and the second one is based on a temporal decomposition of the problem. Local branching is very efficient in finding good feasible solutions when compared to a classical branch-and-bound...

Solving a possibilistic linear program through compromise programming.

Mariano Jiménez López, María Victoria Rodríguez Uría, María del Mar Arenas Parra, Amelia Bilbao Terol (2000)

Mathware and Soft Computing

In this paper we propose a method to solve a linear programming problem involving fuzzy parameters whose possibility distributions are given by fuzzy numbers. To address the above problem we have used a preference relationship of fuzzy numbers that leads us to a solving method that produces the so-called α-degree feasible solutions. It must be pointed out that the final solution of the problem depends critically on this degree of feasibility, which is in conflict with the optimal value of the objective...

Stochastic goal programming wth recourse

Antonio Heras Martínez, Ana García Aguado (1998)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

In this article we discuss several alternative formulations for Stochastic Goal Programming. Only one of these models, which is a particular case of the Stochastic Programs with Recourse, is also compatible with Bayesian Decision Theory. Moreover, it is posible to approximate its solutions by means of an iterative algorithm.

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