On solving Linear Complementarity Problems by DC programming and DCA

Computational Optimization and Applications

Volumn 50, Issue 3, 2011, Pages 507-524

  Le Thi, Hoai An ^a   Pham Dinh, Tao ^b  

^a UNIVERSITÉ DE LORRAINE   (France)

^b UNIVERSITÉ ET INSA DE ROUEN   (France)

Author keywords

DC programming; DCA; LCP

Indexed keywords

D-C PROGRAMMING; DC ALGORITHM; DCA; DIFFERENCE OF CONVEX FUNCTIONS; LCP; LINEAR COMPLEMENTARITY; LINEAR COMPLEMENTARITY PROBLEMS; LINEAR PROGRAMS; NUMERICAL EXPERIMENTS; OPTIMIZATION MODELS; QUADRATIC PROGRAMS; SPEED OF CONVERGENCE; TEST PROBLEM;

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS;

PROBLEM SOLVING;

EID: 84855351342     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-011-9398-y     Document Type: Conference Paper

References (25)

1. B.-H. Ahn 1983 Iterative methods for linear complementarity problems with upper bounds on primary variables Math. Program. 26 295 315 0506.90081 10.1007/BF02591868
2. 0 matrix linear complementarity problem SIAM J. Optim. 11 2 341 363 1787264 0994.65077 10.1137/S1052623498335080 (Pubitemid 33357976)
3. Cottle, R., Pang, J., Stone, R.: The Linear Complementarity Problem. Academic Press, San Diego (1992)
4. Y. Fathi 1979 Computational complexity of LCPs associated with positive definite symmetric matrices Math. Program. 17 335 344 550849 0421.90072 10.1007/BF01588254 (Pubitemid 10439058)
5. L. Fernandes A. Friedlander M.C. Guedes J. Judice 2001 Solution of a general linear complementarity problem using smooth optimization and its application to bilinear programming and LCP Appl. Math. Optim. 43 1 19 1804392 1033.90132 10.1007/s002450010021 (Pubitemid 32874183)
6. Fletcher, R.: Practical Methods of Optimization. Wiley, New York (1987). ISBN13:978-0471494638
7. Floudas, C.A., et al.: Handbook of Test Problems in Local and Global Optimization. Nonconvex Optimization and Its Applications, vol. 33. Kluwer Academic, Dordrecht (1999). XV
8. J. Judice A.M. Faustino I.M. Ribeiro 2002 On the solution of NP-hard linear complementarity problems Top 10 1 125 145 1915697 1006.90082 10.1007/BF02578944
9. C. Geiger C. Kanzow 1996 On the resolution of monotone complementarity problems Comput. Optim. Appl. 5 2 155 173 1373295 0859.90113 10.1007/BF00249054 (Pubitemid 126708357)
10. Krause, N., Singer, Y.: Leveraging the margin more carefully In: Proceedings of the 21st International Conference on Machine Learning, ICML, 2004, Banff, Alberta, Canada, p. 63 (2004). ISBN:1-58113-828-5
11. H.A. Le Thi T. Pham Dinh 1997 Solving a class of linearly constrained indefinite quadratic problems by DC algorithms J. Glob. Optim. 11 3 253 285 0905.90131 10.1023/A:1008288411710
12. H.A. Le Thi T. Pham Dinh 2005 The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems Ann. Oper. Res. 133 23 46 2119311 1116.90122 10.1007/s10479-004-5022-1 (Pubitemid 40389738)
13. Y. Liu X. Shen H. Doss 2005 Multicategory ψ-learning and support vector machine: computational tools J. Comput. Graph. Stat. 14 219 236 2137899 10.1198/106186005X37238 (Pubitemid 40447834)
14. Murty, K.G.: Linear Complementarity, Linear and Nonlinear Programming. Sigma Series in Applied Mathematics, vol. 3. Heldermann, Berlin (1988)
15. Pardalos, P.M.: The linear complementarity problem. In: Gomez, S., Hennart, J.P. (eds.) Advances in Optimization and Numerical Analysis, pp. 39-49. Kluwer Academic, Norwell (1994).
16. P.M. Pardalos J.B. Rosen 1988 Global optimization approach to the linear complementarity problem SIAM J. Sci. Stat. Comput. 9 2 341 353 930050 10.1137/0909022
17. P.M. Pardalos S.A. Vavasis 1991 Quadratic programming with one negative eigenvalue is NP-hard J. Glob. Optim. 1 1 15 22 1263835 0755.90065 10.1007/BF00120662
18. P.M. Pardalos Y. Ye 1991 A class of linear complementarity problems solvable in polynomial time Linear Algebra Appl. 152 3 17 1107542 0742.65054 10.1016/0024-3795(91)90267-Z
19. T. Pham Dinh H.A. Le Thi 1997 Convex analysis approach to d.c. programming: theory, algorithms and applications Acta Math. Vietnam. 22 1 289 355 1479751 0895.90152
20. T. Pham Dinh H.A. Le Thi 1998 D.c. optimization algorithms for solving the trust region subproblem SIAM J. Optim. 8 2 476 505 1618531 0913.65054 10.1137/S1052623494274313 (Pubitemid 128078209)
21. Ronan, C., Fabian, S., Jason, W., Léon, B.: Trading convexity for scalability. In: Proceedings of the 23rd International Conference on Machine Learning, ICML 2006, Pittsburgh, Pennsylvania, pp. 201-208 (2006). ISBN:1-59593-383-2
22. Schnörr, C., Schüle, T., Weber, S.: Variational reconstruction with DC-programming. In: Herman, G.T., Kuba, A. (eds.) Advances in Discrete Tomography and Its Applications. Birkhäuser, Boston (2007)
23. T. Schüle C. Schnörr S. Weber J. Hornegger 2005 Discrete tomography by convex-concave regularization and d.c. programming Discrete Appl. Math. 151 229 243 2173313 1131.68571 10.1016/j.dam.2005.02.028 (Pubitemid 41329795)
24. H. Sherali R. Krishnamurty F. Al-Khayyal 1998 Enumeration approach for linear complementarity problems based on a reformulation-linearization technique J. Optim. Theory Appl. 99 481 507 1657057 0911.90328 10.1023/A:1021734613201 (Pubitemid 128433484)
25. 0 LCPs SIAM J. Optim. 13 4 1195 1221 2005924 1039.90081 10.1137/S1052623401384151 (Pubitemid 37395693)