A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems (Lecture Notes in Computer Science, 538, Band 538) - Softcover

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

Softcover

ISBN 10: 3540545093 ISBN 13: 9783540545095

Verlag: Springer, 2008

Inhaltsangabe

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 zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2008
• Sprache: Englisch
• ISBN 10: 3540545093
• ISBN 13: 9783540545095
• Einband: Taschenbuch
• Anzahl der Seiten: 120
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland