A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems

by Masakazu Kojima, Nimrod Megiddo, Toshihito Noma, Akiko Yoshise

Overview

Following Karmarkar's 1984 linear programming algorithm, numerous interior-point algorithms have been proposed for various mathematical programming problems such as linear programming, convex quadratic programming and convex programming in general. This monograph presents a study of interior-point algorithms for the linear complementarity problem (LCP) which is known as a mathematical model for primal-dual pairs of linear programs and convex quadratic programs. A large family of potential reduction algorithms is presented in a unified way for the class of LCPs where the underlying matrix has nonnegative principal minors (P0-matrix). This class includes various important subclasses such as positive semi-definite matrices, P-matrices, P*-matrices introduced in this monograph, and column sufficient matrices. The family contains not only the usual potential reduction algorithms but also path following algorithms and a damped Newton method for the LCP. The main topics are global convergence, global linear convergence, and the polynomial-time convergence of potential reduction algorithms included in the family.

Product Details

ISBN-13:	9783540545095
Publisher:	Springer Berlin Heidelberg
Publication date:	10/28/1991
Series:	Lecture Notes in Computer Science , #538
Edition description:	1991
Pages:	112
Product dimensions:	6.10(w) x 9.17(h) x 0.01(d)

Table of Contents

Summary.- The class of linear complementarity problems with P 0-matrices.- Basic analysis of the UIP method.- Initial points and stopping criteria.- A class of potential reduction algorithms.- Proofs of convergence theorems.