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Unified Approach to Interior Point Algorithms for Linear Complementarity Problems by Masakazu Kojima & Nimrod Megiddo & Toshihito Noma
This monograph presents a study of interior-point algorithms for the linear complementarity problem, known as a mathematical model for primal-dual pairs of linear programs and convex quadratic programs. A large class of potential reduction algorithms is presented in a unified way.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. |
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| Author(s) : Nimrod Megiddo | Format : Paperback Book |
| ISBN-10 : 3540545093 | ISBN-13 : 9783540545095 |
| RRP : £32.50 | Best available price : £28.97 / $49.92 |
| Prices as of : 12/08/2008 10:44:42 PM BST check live prices | |
Product Details:
Series Title : Lecture Notes in Computer Science
Country Publication : Germany
Publication Date : 01/09/1991
Publisher : Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Page Length : VIII, 108mm
Page Size : 216mm