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＜電子ブック＞
A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems / by Masakazu Kojima, Nimrod Megiddo, Toshihito Noma, Akiko Yoshise
(Lecture Notes in Computer Science. ISSN:16113349 ; 538)

版	1st ed. 1991.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1991
本文言語	英語
大きさ	VIII, 112 p : online resource
著者標目	*Kojima, Masakazu author Megiddo, Nimrod author Noma, Toshihito author Yoshise, Akiko author SpringerLink (Online service)
件　名	LCSH:Mathematics LCSH:Numerical analysis LCSH:System theory LCSH:Control theory LCSH:Mathematical optimization LCSH:Calculus of variations FREE:Applications of Mathematics FREE:Numerical Analysis FREE:Systems Theory, Control FREE:Calculus of Variations and Optimization
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/3-540-54509-3

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