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A LARGE-UPDATE INTERIOR POINT ALGORITHM FOR P*(k) LCP BASED ON A NEW KERNEL FUNCTION

조경미|조유영
영남수학회 (Youngnam Mathematical Society)|2010.01|East Asian Mathematical Journal|제26권 제1호|pp. 9-23

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참고문헌

키워드

complexityprimal-dual interior point methodkernel functionpolynomial algorithmlinear optimization problem
주제분류수학

초록

In this paper we generalize large-update primal-dual interior point methods for linear optimization problems in [2] to the P* (k) linear complementarity problems based on a new kernel function which includes the kernel function in [2] as a special case. The kernel function is neither self-regular nor eligible. Furthermore, we improve the complexity result in [2] from O([수식]) to O([수식]) .

Abstract

In this paper we generalize large-update primal-dual interior point methods for linear optimization problems in [2] to the P* (k) linear complementarity problems based on a new kernel function which includes the kernel function in [2] as a special case. The kernel function is neither self-regular nor eligible. Furthermore, we improve the complexity result in [2] from O([수식]) to O([수식]) .

참고문헌 (15)

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  2. Y. Q. Bai, "A comparative study of kernel functions for primal-dual interior-point algo-rithms in linear optimization", Siam J. on Optimization, 15, pp.101~128 (2004)
  3. G. M. Cho, "A new large-update interior point algorithm for P linear complementar-ity problems", Journal of Computational and Applied Mathematics, 216, pp.256~278 (2008)
  4. G. M. Cho, "A new large-update interior point algorithm for PLCPs based on kernel functions", Applied Mathematics and Computation, 182, pp.1169~1183 (2006)
  5. R. W. Cottle, "The linear complementarity problem" (1992), Aca-demic Press
  6. M. El Ghami, "A polynomial-time algorithm for linear optimization based on a new class of kernel functions", Journal of Computational and Applied Mathematics, 224, pp.500~513 (2009)
  7. T. Illes, "A Mizuno-Todd-Ye type preditor-corrector algorithm for su-cient linear complementarity problems", European Journal of Operational Research, 181, pp.1097~1111 (2007)
  8. M. Kojima, "A unied approach to interior point algorithms for linear complementarity problems, Vol.538, Lecture Notes in Computer Science" (1991), Springer-Verlag
  9. S. G. Nash, "Linear and nonlinear programming" (1996), McGraw-Hill
  10. Y. E. Nesterov, "Interior point polynomial algorithms in convex programming" (1994), SIAM Studies in Applied Mathematics
  11. J. Peng, "Self-regular functions and new search directions for linear and semidenite optimization", Mathematical Programming, 93, pp.129~171 (2002)
  12. J. Peng, "Primal-dual interior-point methods for second-order conic optimization based on self-regular proximities", SIAM J. Optim., 13, pp.179~203 (2002)
  13. J. Peng, "Self-Regularity, A new paradigm for primal-dual interior-point algorithms" (2002), Princeton University Press
  14. C. Roos, "Theory and algorithms for linear optimization, An interior approach" (1997), John Wiley & Sons
  15. S. J. Wright, "Primal-dual interior-point methods" (1997), SIAM

관련 논문AI추천

Complexity analysis of IPM for P*(κ) LCPs based on eligible kernel functions김민경, 조경미영남수학회 · East Asian Mathematical Journal2009 · 제25권 제1호NEW PRIMAL-DUAL INTERIOR POINT METHODS FOR P*(κ) LINEAR COMPLEMENTARITY PROBLEMS김민경, 조경미대한수학회 · 대한수학회논문집2010 · 제25권 제4호New 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 제3호An adaptive primal-dual full-Newton step infeasible interior-point algorithm for linear optimizationHossein Mansouri, Maryam Zangiabadi, Soodabeh Asadi대한수학회 · 대한수학회보2016 · 제53권 제6호

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