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论文类型：期刊论文

发表时间：2007-07-15

发表刊物：APPLIED MATHEMATICS AND COMPUTATION

收录刊物：SCIE、EI、Scopus

卷号：190

期号：2

页面范围：1030-1039

ISSN号：0096-3003

关键字：nonlinear equality-constrained optimization; constraint qualification; differential equation; asymptotical stability; equilibrium point

摘要：This paper presents two differential systems, involving first and second order derivatives of problem functions, respectively, for solving equality-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, we construct algorithms in which directions are computed by these two systems and the stepsizes are generated by Armijo line search to solve the original equality-constrained optimization problem. The constructed algorithms and the Runge-Kutta method are employed to solve the Euler discrete schemes and the differential equation systems, respectively. We prove that the discrete scheme based on the differential equation system with the second order information has the locally quadratic convergence rate under the local Lipschitz condition. The numerical results given here show that Runge-Kutta method has better stability and higher precision and the numerical method based on the differential equation system with the second information is faster than the other one. (c) 2006 Elsevier Inc. All rights reserved.