A QUADRATICALLY CONVERGENT O((KAPPA+1)ROOT-N L)-ITERATION ALGORITHM FOR THE P-ASTERISK(KAPPA)-MATRIX LINEAR COMPLEMENTARITY-PROBLEM

被引：49

作者：

MIAO, JM

机构：

[1] RUTCOR - Rutgers Center for Operations Research, Rutgers University, New Brunswick, 08903-5062, NJ

来源：

MATHEMATICAL PROGRAMMING | 1995年 / 69卷 / 03期

关键词：

LINEAR COMPLEMENTARITY PROBLEM; INTERIOR-POINT ALGORITHM; QUADRATIC CONVERGENCE; POLYNOMIAL-TIME ALGORITHM;

D O I：

10.1007/BF01585565

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

An interior-point predictor-corrector algorithm for the P*(kappa)-matrix linear complementarity problem is proposed. The algorithm is an extension of Mizuno-Todd-Ye's predictor-corrector algorithm for linear programming problem. The extended algorithm is quadratically convergent with iteration complexity O((kappa + 1)root nL). It is the first polynomially and quadratically convergent algorithm for a class of LCPs that are not necessarily monotone.

引用

页码：355 / 368

页数：14

共 10 条

[1] A QUADRATICALLY CONVERGENT O(ROOT-N L)-ITERATION ALGORITHM FOR LINEAR-PROGRAMMING
YE, Y
GULER, O
TAPIA, RA
ZHANG, Y
MATHEMATICAL PROGRAMMING, 1993, 59 (02) : 151 - 162
[2] Quadratically convergent O(√n L)-iteration algorithm for linear programming
Ye, Y.
Guler, O.
Tapia, R.A.
Zhang, Y.
Mathematical Programming, Series A, 1993, 59 (02): : 151 - 162
[3] AN O(N3L) ALGORITHM USING A SEQUENCE FOR A LINEAR COMPLEMENTARITY-PROBLEM
MIZUNO, S
JOURNAL OF THE OPERATIONS RESEARCH SOCIETY OF JAPAN, 1990, 33 (01) : 66 - 75
[4] SUPERLINEARLY CONVERGENT O(ROOT-NL)-ITERATION INTERIOR-POINT ALGORITHMS FOR LINEAR-PROGRAMMING AND THE MONOTONE LINEAR COMPLEMENTARITY-PROBLEM
MCSHANE, K
SIAM JOURNAL ON OPTIMIZATION, 1994, 4 (02) : 247 - 261
[5] AN O(N3L) ADAPTIVE PATH FOLLOWING ALGORITHM FOR A LINEAR COMPLEMENTARITY-PROBLEM
MIZUNO, S
TODD, MJ
MATHEMATICAL PROGRAMMING, 1991, 52 (03) : 587 - 595
[6] AN O(SQUARE-ROOT-N L) ITERATION POTENTIAL REDUCTION ALGORITHM FOR LINEAR COMPLEMENTARITY-PROBLEMS
KOJIMA, M
MIZUNO, S
YOSHISE, A
MATHEMATICAL PROGRAMMING, 1991, 50 (03) : 331 - 342
[7] A New Full-Newton Step O(n) Infeasible Interior-Point Algorithm for P-* (kappa)-horizontal Linear Complementarity Problems
Asadi, Soodabeh
Mansouri, Hossein
COMPUTER SCIENCE JOURNAL OF MOLDOVA, 2014, 22 (01) : 37 - 61
[8] AN ASYMPTOTICAL O((k + 1)n~3L) AFFINE SCALING ALGORITHM FOR THE P*(k)-MATRIX LINEAR COMPLEMENTRITY PROBLEM
Zhe-ming Wang (Department of Statistics and Operations Research
JournalofComputationalMathematics, 2001, (02) : 177 - 186
[9] An asymptotical O((k+1)n3L) affine scaling algorithm for the P*(k)-matrix linear complementrity problem
Wang, ZM
Huang, ZH
Zhou, KP
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2001, 19 (02) : 177 - 186
[10] An O(nL)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\sqrt{n}L)$$\end{document} iteration Mehrotra-type predictor-corrector algorithm for monotone linear complementarity problem
Changhe Liu
Youlin Shang
Hongwei Liu
Optimization Letters, 2016, 10 (3) : 619 - 634

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