A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems

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

112 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: Lecture Notes in Computer Science
• Themen: Mathematik und Naturwissenschaften Mathematik Angewandte Mathematik
• ISBN: 9783540545095
• Sprache: Englisch
• Erscheinungsdatum: 25.09.1991
• Größe: 23.3 x 15.5 cm
• Verlag: Springer Berlin