A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems

Following Karmarkar's 1984 linear programming algorithm,numerous interior-point algorithms have been proposed forvarious mathematical programming problems such as linearprogramming, convex quadratic programming and convexprogramming in general. This monograph presents a study ofinterior-point algorithms for the linear complementarityproblem (LCP) which is known as a mathematical model forprimal-dual pairs of linear programs and convex quadraticprograms. A large family of potential reduction algorithmsis presented in a unified way for the class of LCPs wherethe underlying matrix has nonnegative principal minors(P0-matrix). This class includes various importantsubclasses such as positive semi-definite matrices,P-matrices, P*-matrices introduced in this monograph, andcolumn sufficient matrices. The family contains not only theusual potential reduction algorithms but also path followingalgorithms and a damped Newton method for the LCP. The maintopics are global convergence, global linear convergence,and the polynomial-time convergence of potential reductionalgorithms included in the family.

List 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.

Product details

• Authors: Masakaz Kojima, Masakazu Kojima, Nimro Megiddo, Nimrod Megiddo, Toshihito Noma, Toshihito e Noma, Akiko Yoshise
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.1960
• EAN: 9783540545095
• ISBN: 978-3-540-54509-5
• No. of pages: 112
• Weight: 212 g
• Illustrations: VIII, 112 p.
• Series: Lecture Notes in Computational Science and Engineering; Lecture Notes in Computer Science; Lecture Notes in Computational Science and Engineering
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra