Lecture Notes in Computer Science

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

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.

Details

Published by: Springer

Publication Date: 1991-09-25

Format: Paperback

ISBN-13: 9783540545095

DOI: 10.1007/3-540-54509-3

Dimensions: 233cm x155cm

Pages: 112