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A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems : Lecture Notes in Computer Science - Masakazu Kojima

A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems

Lecture Notes in Computer Science

Paperback Published: 25th September 1991
ISBN: 9783540545095
Number Of Pages: 112

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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.

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.

ISBN: 9783540545095
ISBN-10: 3540545093
Series: Lecture Notes in Computer Science
Audience: General
Format: Paperback
Language: English
Number Of Pages: 112
Published: 25th September 1991
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 0.66
Weight (kg): 0.19