CONTINUOUS HOMOTOPIES FOR THE LINEAR COMPLEMENTARITY-PROBLEM

作     者：WATSON, LT BIXLER, JP POORE, AB 

作者机构：COLORADO STATE UNIVDEPT MATHFT COLLINSCO 80523 

出 版 物：《SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS》 (工业与应用数学会矩阵分析和应用杂志)

年 卷 期：1989年第10卷第2期

页      面：259-277页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：65H10 65L10 65L60 homotopy algorithm globally convergent linear complementarity problem fixed point expanded Lagrangian nonlinear equations 

摘      要：There are various formulations of the linear complementarity problem as a Kakutani fixed point problem, a constrained optimization, or a nonlinear system of equations. These formulations have remained a curiosity since not many people seriously thought that a linear combinatorial problem should be converted to a nonlinear problem. Recent advances in homotopy theory and new mathematical software capabilities such as HOMPACK indicate that continuous nonlinear formulations of linear and combinatorial problems may not be farfetched. Several different types of continuous homotopies for the linear complementarity problem are presented and analyzed here, with some numerical results. The homotopies with the best theoretical properties (global convergence and no singularities along the zero curve) turn out to also be the best in practice.