A Unified approach to interior point algorithms for linear complementarity problems
著者
書誌事項
A Unified approach to interior point algorithms for linear complementarity problems
（Lecture notes in computer science, 538）
Springer-Verlag, c1991
- : gw
- : us
- タイトル別名
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Interior point algorithms for linear complimentarity problems
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注記
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
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.
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