Browse > Article
http://dx.doi.org/10.4134/CKMS.c180109

SQUARE QUADRATIC PROXIMAL METHOD FOR NONLINEAR COMPLIMENTARITY PROBLEMS  

Bnouhachem, Abdellah (Equipe MAISI Ibn Zohr University)
Ou-yassine, Ali (Ibn Zohr University Faculte Polydisciplinaire Ouarzazate)
Publication Information
Communications of the Korean Mathematical Society / v.34, no.2, 2019 , pp. 671-684 More about this Journal
Abstract
In this paper, we propose a new interior point method for solving nonlinear complementarity problems. In this method, we use a new profitable searching direction and instead of using the logarithmic quadratic term, we use a square root quadratic term. We prove the global convergence of the proposed method under the assumption that F is monotone. Some preliminary computational results are given to illustrate the efficiency of the proposed method.
Keywords
nonlinear complementarity problems; monotone operator; square root quadratic term; interior point method;
Citations & Related Records
연도 인용수 순위
  • Reference
1 B. He, Z. Yang, and X. Yuan, An approximate proximal-extragradient type method for monotone variational inequalities, J. Math. Anal. Appl. 300 (2004), no. 2, 362-374.   DOI
2 D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and their Applications, Pure and Applied Mathematics, 88, Academic Press, Inc., New York, 1980.
3 M. A. Noor and A. Bnouhachem, Modified proximal-point method for nonlinear complementarity problems, J. Comput. Appl. Math. 197 (2006), no. 2, 395-405.   DOI
4 H. Yang and M. G. H. Bell, Traffc restraint, road pricing and network equilibrium, Transportation Research B 31 (1997), 303-314.   DOI
5 X. Yuan, The prediction-correction approach to nonlinear complementarity problems, European J. Oper. Res. 176 (2007), no. 3, 1357-1370.   DOI
6 A. Auslender, M. Teboulle, and S. Ben-Tiba, Interior proximal and multiplier methods based on second order homogeneous kernels, Math. Oper. Res. 24 (1999), no. 3, 645-668.   DOI
7 A. Auslender, M. Teboulle, and S. Ben-Tiba, A logarithmic-quadratic proximal method for variational inequalities, Comput. Optim. Appl. 12 (1999), no. 1-3, 31-40.   DOI
8 A. Bnouhachem, M. A. Noor, and S. Zhaohan, A new logarithmic-quadratic proximal method for nonlinear complementarity problems, Appl. Math. Comput. 215 (2009), no. 2, 695-706.   DOI
9 A. Bnouhachem and M. A. Noor, A new predicto-corrector method for pseudomonotone nonlinear complementarity problems, Int. J. Comput. Math. 85 (2008), no. 7, 1023-1038.   DOI
10 A. Bnouhachem, M. A. Noor, A. Massaq, and S. Zhaohan, A note on LQP method for nonlinear complimentarity problems, Adv. Model. Optim. 14 (2012), no. 1, 269-283.
11 A. Bnouhachem, A. Ou-yassine, M. A. Noor, and G. Lakhnati G, Modified LQP method with a new search direction for nonlinear complimentarity problems, Appl. Math. Inf. Sci. 10 (2016), no. 4, 1375-1383.   DOI
12 A. Bnouhachem and X. M. Yuan, Extended LQP method for monotone nonlinear complementarity problems, J. Optim. Theory Appl. 135 (2007), no. 3, 343-353.   DOI
13 M. C. Ferris and J. S. Pang, Engineering and economic applications of complementarity problems, SIAM Rev. 39 (1997), no. 4, 669-713.   DOI
14 A. Bnouhachem, An LQP method for pseudomonotone variational inequalities, J. Global Optim. 36 (2006), no. 3, 351-363.   DOI
15 P. T. Harker and J.-S. Pang, A damped-Newton method for the linear complementarity problem, in Computational solution of nonlinear systems of equations (Fort Collins, CO, 1988), 265-284, Lectures in Appl. Math., 26, Amer. Math. Soc., Providence, RI. 1990.
16 B. He, L. Liao, and X. Yuan, A LQP based interior prediction-correction method for nonlinear complementarity problems, J. Comput. Math. 24 (2006), no. 1, 33-44.
17 B. He, Y. Xu, and X. Yuan, A logarithmic-quadratic proximal prediction-correction method for structured monotone variational inequalities, Comput. Optim. Appl. 35 (2006), no. 1, 19-46.   DOI