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Smoothing functions and algorithm for nonsymmetric circular cone complementarity problems

Jingyong Tang, Yuefen Chen (2022)

Applications of Mathematics

There has been much interest in studying symmetric cone complementarity problems. In this paper, we study the circular cone complementarity problem (denoted by CCCP) which is a type of nonsymmetric cone complementarity problem. We first construct two smoothing functions for the CCCP and show that they are all coercive and strong semismooth. Then we propose a smoothing algorithm to solve the CCCP. The proposed algorithm generates an infinite sequence such that the value of the merit function converges...

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 no dominadas en problemas multiobjetivo.

Luis Coladas Uría (1981)

Trabajos de Estadística e Investigación Operativa

La Teoría de Estructuras de Dominación, introducida por P. L. Yu como nuevo procedimiento de solución a problemas multiobjetivo, presenta bastantes lagunas, debidas sin duda a la novedad del tema. Nos hemos propuesto en este trabajo caracterizar completamente los puntos no dominados, por distintos procedimientos, así como seleccionar entre ellos un subconjunto más deseable ("soluciones propias"). Se abordan también condiciones para soluciones no dominadas en el espacio de decisiones.

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...

Solution of a fractional combinatorial optimization problem by mixed integer programming

Alain Billionnet, Karima Djebali (2006)

RAIRO - Operations Research

Fractionnal mathematical programs appear in numerous operations research, computer science and economic domains. We consider in this paper the problem of maximizing the sum of 0–1 hyperbolic ratios (SRH). In contrast to the single ratio problem, there has been little work in the literature concerning this problem. We propose two mixed-integer linear programming formulations of SRH and develop two different strategies to solve them. The first one consists in using directly a general-purpose mixed-integer...

Solution set in a special case of generalized Nash equilibrium games

Josef Cach (2001)

Kybernetika

A special class of generalized Nash equilibrium problems is studied. Both variational and quasi-variational inequalities are used to derive some results concerning the structure of the sets of equilibria. These results are applied to the Cournot oligopoly problem.

Solvability of the power flow problem in DC overhead wire circuit modeling

Jakub Ševčík, Lukáš Adam, Jan Přikryl, Václav Šmídl (2021)

Applications of Mathematics

Proper traffic simulation of electric vehicles, which draw energy from overhead wires, requires adequate modeling of traction infrastructure. Such vehicles include trains, trams or trolleybuses. Since the requested power demands depend on a traffic situation, the overhead wire DC electrical circuit is associated with a non-linear power flow problem. Although the Newton-Raphson method is well-known and widely accepted for seeking its solution, the existence of such a solution is not guaranteed. Particularly...

Solving a class of non-convex quadratic problems based on generalized KKT conditions and neurodynamic optimization technique

Alaeddin Malek, Najmeh Hosseinipour-Mahani (2015)

Kybernetika

In this paper, based on a generalized Karush-Kuhn-Tucker (KKT) method a modified recurrent neural network model for a class of non-convex quadratic programming problems involving a so-called Z -matrix is proposed. The basic idea is to express the optimality condition as a mixed nonlinear complementarity problem. Then one may specify conditions for guaranteeing the global solutions of the original problem by using results from the S-lemma. This process is proved by building up a dynamic system from...

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