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