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

Alaeddin Malek; Najmeh Hosseinipour-Mahani

Kybernetika (2015)

  • Volume: 51, Issue: 5, page 890-908
  • ISSN: 0023-5954

Abstract

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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 the optimality condition whose equilibrium point is exactly the solution of the mixed nonlinear complementarity problem. By the study of the resulting dynamic system it is shown that under given assumptions, steady states of the dynamic system are stable. Numerical simulations and comparisons with the other methods are presented to illustrate the efficiency of the practical technique that is proposed in this paper.

How to cite

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Malek, Alaeddin, and Hosseinipour-Mahani, Najmeh. "Solving a class of non-convex quadratic problems based on generalized KKT conditions and neurodynamic optimization technique." Kybernetika 51.5 (2015): 890-908. <http://eudml.org/doc/276322>.

@article{Malek2015,
abstract = {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 the optimality condition whose equilibrium point is exactly the solution of the mixed nonlinear complementarity problem. By the study of the resulting dynamic system it is shown that under given assumptions, steady states of the dynamic system are stable. Numerical simulations and comparisons with the other methods are presented to illustrate the efficiency of the practical technique that is proposed in this paper.},
author = {Malek, Alaeddin, Hosseinipour-Mahani, Najmeh},
journal = {Kybernetika},
keywords = {non-convex quadratic optimization; recurrent neural network model; global optimality conditions; global convergence},
language = {eng},
number = {5},
pages = {890-908},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Solving a class of non-convex quadratic problems based on generalized KKT conditions and neurodynamic optimization technique},
url = {http://eudml.org/doc/276322},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Malek, Alaeddin
AU - Hosseinipour-Mahani, Najmeh
TI - Solving a class of non-convex quadratic problems based on generalized KKT conditions and neurodynamic optimization technique
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 5
SP - 890
EP - 908
AB - 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 the optimality condition whose equilibrium point is exactly the solution of the mixed nonlinear complementarity problem. By the study of the resulting dynamic system it is shown that under given assumptions, steady states of the dynamic system are stable. Numerical simulations and comparisons with the other methods are presented to illustrate the efficiency of the practical technique that is proposed in this paper.
LA - eng
KW - non-convex quadratic optimization; recurrent neural network model; global optimality conditions; global convergence
UR - http://eudml.org/doc/276322
ER -

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