A Unified Approach To Interior Point Algorithms For Linear Complementarity Problems -

M. Yoshise A. Kojima

ISBN 10: 0387545093 / ISBN 13: 9780387545097

Published by Springer-Verlag, 1991

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Bibliographic Details

• Title: A Unified Approach To Interior Point Algorithms For Linear Complementarity Problems -
• Publisher: Springer-Verlag
• Publication Date: 1991
• Language: English
• ISBN 10: 0387545093
• ISBN 13: 9780387545097
• Binding: Soft cover
• Condition: New

About this title

Synopsis

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.