On semidefinite linear complementarity problems

Mathematical Programming, Series B

Volumn 88, Issue 3, 2000, Pages 575-587

  Gowda, M Seetharama ^a   Song, Yoon ^a  

^a UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

Author keywords

GUS property; Lyapunov; P property; Semidefinite linear complementarity problem

Indexed keywords

EID: 0013349755     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00011387     Document Type: Article

References (30)

1. Alizadeh, F. (1995): Interior point methods in semidefinite programming with application to combinatorial optimization. SIAM J. Optim. 5, 13-51
2. Bellman, R. (1995): Introduction to Matrix Analysis. Society for Industrial and Applied Mathematics, Philadelphia (Republication of 1960 McGraw-Hill Edition)
3. Berman, A., Plemmons, R.J. (1994): Nonnegative Matrices in the Mathematical Sciences. Society for Industrial and Applied Mathematics, Philadelphia
4. Borwein, J.M., Dempster, M.A.H. (1989): The linear order complementarity problem. Math. Oper. Res. 14, 534-558
5. Boyd, S., Ghaoui, L. El, Feron, E., Balakrishnan, V. (1994): Linear Matrix Inequalities in System and Control Theory, Society for Industrial and Applied Mathematics, Philadelphia
6. Cottle, R.W., Pang, J.-S., Stone, R.E. (1992): The Linear Complementarity Problem. Academic Press, Boston
7. Faraut, J., Koranyi, A. (1994): Analysis on Symmetric Cones, Oxford University Press, Oxford
8. Ferris, M.C., Pang, J.-S., eds. (1997): Complementarity and Variational Problems (State of the Art). Society for Industrial and Applied Mathematics, Philadelphia
9. Ferris, M.C., Pang, J.-S. (1997): Engineering and economic applications of complementarity problems. SIAM Rev. 39, 669-713
10. Gantmacher, F.R. (1959): Theory of Matrices, Vol. II. Chelsea Publishing Company, New York
11. Gowda, M.S., Sznajder, R. (1994): The generalized order linear complementarity problem. SIAM J. Matrix Anal. Appl. 15, 779-795
12. Harker, P.T., Pang, J.-S. (1990): Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Math. Program. 48, 161-220
13. Hershkowitz, D. (1992): Recent directions in matrix stability. Linear Algebra Appl. 171, 161-186
14. Horn, R.A., Johnson, C.R. (1985): Matrix Analysis. Cambridge University Press, Cambridge
15. Horn, R.A., Johnson, C.R. (1991): Topics in Matrix Analysis. Cambridge University Press, Cambridge
16. Isac, G. (1992): Complementarity Problems. Lecture notes in Mathematics, Springer-Verlag, New York
17. Karamardian, S. (1976): An existence theorem for the complementarity problem. J. Optimization Theory Appl. 19, 227-232
18. Kojima, M., Shindoh, S., Hara, S. (1997): Interior-point methods for the monotone semidefinite linear complementarity problems. SIAM J. Optim. 7, 86-125
19. Lyapunov, M.A. (1907): Probléme général de la stabilité des mouvement. Ann. Fac. Sci. Toulouse 9, 203-474
20. (French, translation of the original paper published in 1893 in Comm. Soc. math. Kharkow; reprinted as Vol. 17 in Annals of Mathematics Study, Princeton University Press, Princeton, New Jersey, 1949)
21. Megiddo, N., Kojima, M. (1977): On the existence and uniqueness of solutions in nonlinear complementarity theory. Math. Program. 12, 110-130
22. Mesbahi, M., Papavassilopoulos, G.P. (1997): A cone programming approach to the bilinear matrix inequality problem and its geometry. Math. Program. 77, 247-272
23. Monteiro, R.D.C., Tsuchiya, T. (1999): Polynomiality of primal-dual algorithms for semidefinite linear complementarity problems based on the Kojima-Shindoh-Hara family of directions. Math. Program. 84, 39-54
24. Overton, M., Wolkowicz, H., eds. (1997): Semidefinite programming. Math. Program. 77, 97-320
25. Qi, H.-D., Chen, X. (1999): Personal Communication, March 10, 1999
26. Ramana, M.V. (1997): An exact duality theory for semidefinite programming and its complexity implications. Math. Program. 77, 129-162
27. Schneider, H. (1997): Lyapunov revisited: Variations on a matrix theme, operators, systems, and linear algebra (Kaiserslautern, 1997). European Consort. Math. Indust., Teubner, Stuttgart. 175-181
28. Shibata, M., Yamashita, N., Fukushima, M. : The extended semidefinite linear complementarity problem, A reformulation approach. Research Report. Information and Communication System Department, Osaka Gas Co., Ltd, 3-2-27 Minami Chiyozaki, Nishiku, Osaka 550-0023, Japan
29. Tseng, P. (1998): Merit functions for semi-definite complementarity problems. Math. Program. 83, 159-185
30. Vandenberghe, L., Boyd, S. (1996): Semidefinite programming. SIAM Rev. 38, 49-95