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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.
| Autorius: | Masakazu Kojima, Akiko Yoshise, Toshihito Noma, Nimrod Megiddo, |
| Serija: | Lecture Notes in Computer Science |
| Leidėjas: | Springer Berlin Heidelberg |
| Išleidimo metai: | 1991 |
| Knygos puslapių skaičius: | 120 |
| ISBN-10: | 3540545093 |
| ISBN-13: | 9783540545095 |
| Formatas: | 235 x 155 x 7 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems“
