| A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems 1991 Edition Contributor(s): Kojima, Masakazu (Author), Megiddo, Nimrod (Author), Noma, Toshihito (Author) |
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ISBN: 3540545093 ISBN-13: 9783540545095 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback Published: September 1991 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Number Systems - Mathematics | Applied - Mathematics | Linear & Nonlinear Programming |
| Dewey: 519.72 |
| Series: Lecture Notes in Computer Science |
| Physical Information: 0.26" H x 6.14" W x 9.21" (0.41 lbs) 112 pages |