A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems by Masakazu KojimaA Unified Approach to Interior Point Algorithms for Linear Complementarity Problems by Masakazu Kojima

A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems

byMasakazu Kojima, Nimrod Megiddo, Toshihito Noma

Paperback | September 25, 1991

Pricing and Purchase Info

$104.20 online 
$116.95 list price save 10%
Earn 521 plum® points

Prices and offers may vary in store

Quantity:

In stock online

Ships free on orders over $25

Not available in stores

about

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.
Title:A Unified Approach to Interior Point Algorithms for Linear Complementarity ProblemsFormat:PaperbackDimensions:120 pagesPublished:September 25, 1991Publisher:Springer Berlin HeidelbergLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540545093

ISBN - 13:9783540545095

Reviews

Table 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.