Title of Paper:Two differential equation systems for inequality constrained optimization

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Date of Publication:2007-05-15

Journal:APPLIED MATHEMATICS AND COMPUTATION

Included Journals:SCIE、EI、Scopus

Volume:188

Issue:2

Page Number:1334-1343

ISSN No.:0096-3003

Key Words:inequality-constrained optimization; constraint qualification; differential equation; asymptotical stability; equilibrium point

Abstract:This paper presents two differential systems, involving first and second order derivatives of problem functions, respectively, for solving inequality constrained optimization problems. Local minimizers to the optimization problems are proved to be asymptotically stable equilibrium points of the two differential systems. First, the Euler discrete schemes with constant stepsizes for the two differential systems are presented and their convergence theorems are demonstrated. Second, an Euler discrete scheme of the second differential system with an Armijo line search rule, is proposed and proved to have the locally quadratic convergence rate. The numerical results based on solving the second system of differential equations show that the Runge-Kutta method for the second system has good stability and the Euler discrete scheme the Armijo line search rule has fast convergence. (c) 2006 Elsevier Inc. All rights reserved.