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Complexity analysis of IPM for P*(κ) LCPs based on eligible kernel functions

조경미|김민경
영남수학회 (Youngnam Mathematical Society)|2009.03|East Asian Mathematical Journal|제25권 제1호|pp. 55-68

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참고문헌

키워드

complexitykernel functionpolynomial algorithmPrimal-dual interior point methodlarge-updatelinear complementarity problem.
주제분류수학

초록

In this paper we propose new large-update primal-dual interior point algorithms for P*(κ) linear complementarity problems(LCPs). New search directions and proximity measures are proposed based on the kernel function [수식]. We showed that if a strictly feasible starting point is available, then the algorithm has [수식] complexity bound.

Abstract

In this paper we propose new large-update primal-dual interior point algorithms for P*(κ) linear complementarity problems(LCPs). New search directions and proximity measures are proposed based on the kernel function [수식]. We showed that if a strictly feasible starting point is available, then the algorithm has [수식] complexity bound.

참고문헌 (12)

  1. Y.Q. Bai, "A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization", Siam J. on Optimization, 15, pp.101~128 (2005)
  2. G.M. Cho, "Complexity of large-update interior point algo-rithm for P*(k) linear complementarity problems", Computers and Mathematics with Applications, 53, pp.948~960 (2007)
  3. R.W. Cottle, "The linear complementarity problem" (1992), Academic Press Inc
  4. T. Illes, "A Mizuno-Todd-Ye predictor-corrector algorithm for sufficient lin-ear complementarity problems", European Journal of Operational Research, 181(3), pp.1097~1111 (2007)
  5. M. Kojima, "A primal-dual interior point algo-rithm for linear programming, in Progress in mathematical pro-gramming; Interior point related methods", pp.29~47 (1989), Springer Verlag
  6. M. Kojima, "A uni ded approach to interior point algorithms for linear complementarity problems 538, Lecture Notes in Computer Science" (1991), Springer-Verlag
  7. M. Kojima, "A polynomial-time algorithm for a class of linear complementarity problems", Mathematical Programming, 44, pp.1~26 (1989)
  8. M. Kojima, "An O(√nL) iteration potential reduction al-gorithm for linear pomplementarity problems", Mathematical Programming, 50, pp.331~342 (1991)
  9. N. Megiddo, "Pathways to the optimal set in linear programming, in Progress in mathematical programming ; Interior point and related methods", pp.313~358 (1989), Springer Verlag
  10. J. Miao, "A quadratically convergent O((1 +k)√nL)-iteration algorithm for the P*(k)-matrix linear complementarity problem", Mathematical Programming, 69, pp.355~368 (1995)
  11. J. Peng, "Self-regular functions and new search directions for linear and semide nite optimization", Mathematical Programming, 93, pp.129~171 (2002)
  12. C. Roos, "Theory and Algorithms for Linear Optimization" (1997), John Wiley and Sons

관련 논문AI추천

NEW PRIMAL-DUAL INTERIOR POINT METHODS FOR P*(κ) LINEAR COMPLEMENTARITY PROBLEMS김민경, 조경미대한수학회 · 대한수학회논문집2010 · 제25권 제4호A LARGE-UPDATE INTERIOR POINT ALGORITHM FOR P*(k) LCP BASED ON A NEW KERNEL FUNCTION조경미, 조유영영남수학회 · East Asian Mathematical Journal2010 · 제26권 제1호New complexity analysis of primal-dual IMPS for P_(*) LAPS based on large updatesGyeong-Mi Cho, Min-Kyung Kim대한수학회 · 대한수학회보2009 · 제46권 제3호AN ELIGIBLE PRIMAL-DUAL INTERIOR-POINT METHOD FOR LINEAR OPTIMIZATION이용훈, 조경미영남수학회 · East Asian Mathematical Journal2013 · 제29권 제3호A weighted-path following interior-point algorithm for Cartesian P*(k)-LCP over symmetric conesHossein Mansouri, Maryam Zangiabadi, Mohammad Pirhaji대한수학회 · 대한수학회논문집2017 · 제32권 제3호Square quadratic proximal method for nonlinear complimentarity problemsAbdellah Bnouhachem, Ali Ou-yassine대한수학회 · 대한수학회논문집2019 · 제34권 제2호

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