D-orientation sequences for continuous functions and nonlinear complementarity problems

Applied Mathematics and Computation

Volumn 106, Issue 2-3, 1999, Pages 221-235

  Zhao, Yun Bin ^a  

^a INSTITUTE OF APPLIED MATHEMATICS   (China)

Author keywords

Complementarity problems; D orientation sequence; P order generalized coercivity; P* mapping

Indexed keywords

EID: 0002482226     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(98)10125-X     Document Type: Article

References (31)

1. R.W. Cottle, J.S. Pang, R.W. Stone, The Linear Complementarity Problem, Academic Press, Boston, 1992.
2. R.W. Cottle, J.C. Yao, Pseudomonotone complementarity problem in Hilbert space J. Optim. Theory Appl. 75 (1992) 281-295.
3. Eaves B.C. On the basic theorem of complementarity problem. Math. Programming. 1:1971;68-75.
4. Guo J.S., Yao J.C. The variational inequalities, nonlinear complementarity problems. SIAM J. Control Optim. 16:1978;504-511.
5. Harker P.T., Pang J.S. Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications. Math. Programming. 48B:1990;161-220.
6. Hadjisavvas N., Schaible S. Quasimonotone variational inequalities in Banach space. J. Optim. Theory Appl. 90:1996;95-111.
7. G. Isac, Complementarity Problems, Lecture Notes in Mathematics, Springer, Nr. 1528, 1992.
8. Isac G., Bulavski V., Kalashnikov V. Exceptional families, topological degree and complementarity problems. J. Global Optim. 10:1997;1-15.
9. Isac G., Obuchowska W.T. Functions without exceptional family of elements and complementarity problems. J. Optim. Theory Appl. 99:1998;147-163.
10. + , Altman's condition and the complementarity problem J. Fac. Sci. Univ. Tokyo, Sect. IA. 40:1993;1-16.
11. B. Jansen, K. Roos, T. Terlaky, A. Yoshise, Polynomiality of primal dual affine scaling algorithm for nonlinear complementarity problems, TR 95-83, faculty of Technical Mathematics and Computer Science, Delf University of Technology, Delft, the Netherlands, 1995.
12. * -matrix LCP from infeasible starting points Optim. Meth. Software. 6:1995;109-126.
13. Karamardian S. An existence theorem for the complementarity problem. J. Optim. Theory Appl. 19:1976;227-232.
14. Karamardian S. Generalized complementarity problem. J. Optim. Theory Appl. 8:1971;161-167.
15. Karamardian S. The complementarity problem. Math. Programming. 2:1972;107-129.
16. Karamardian S. Complementarity problems over cones with monotone and pseudo- monotone maps. J. Optim. Theory Appl. 18:1976;445-454.
17. D. Kinderlehrer, G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, 1980.
18. M. Kojima, N. Megiddo, T. Noma, A. Yoshise, A Unified Approach to Interior Point Algorithm for Linear Complementarity Problems, Lecture Notes in Computer Sciences, Vol. 538, Springer, New York, 1991.
19. Megiddo N. A monotone complementarity problem with feasible solutions but no complementarity solutions. Math. Programming. 12:1977;131-132.
20. * -mapping matrix linear complementarity problem Math. Programming. 69:1995;355-374.
21. Moré J.J. Classes of function and feasibility condition in nonlinear complementarity problems. Math. Programming. 6:1974;327-338.
22. Moré J.J. Coercivity conditions in nonlinear complementarity problem. SIAM Review. 16:1974;1-16.
23. Smith T.E. A solution condition for complementarity problems, with an application to spatial price equilibrium. Appl. Math. Comput. 15:1984;61-69.
24. Schaible S., Yao J.C. On the equivalence of nonlinear complementarity problems and least element problems. Math. Programming. 70:1995;191-200.
25. *(κ) -matrix LCP from arbitrary positive starting point Math. Programming. 76:1997;223-244.
26. * matrices are just sufficient Linear Algebra Appl. 239:1996;103-108.
27. Väliaho H. Determining the handicap of a sufficient matrix. Linear Algebra Appl. 253:1997;279-298.
28. Y.B. Zhao, J.Y. Han, Exceptional family of elements for a variational inequality and its applications, Technical Report, Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, 1996. Journal of Global Optimization, forthcoming.
29. Zhao Y.B. Exceptional family and finite-dimensional variational inequality over polyhedral sets. Appl. Math. Comput. 87:1997;111-126.
30. Y.B. Zhao, J.Y. Han, H.D. Qi, Exceptional family and existence theorems for variational inequalities, Technical Report, Institute of Applied Mathematics, Chinese Academy of Science, Beijing, China, 1997. Journal of Optimization Theory and Applications, 101 (1999), forthcoming.
31. Y.B. Zhao, J.Y. Han, On the polynomiality of two interior-point methods for non-monotone nonlinear complementarity problems, Technical Report, Institute of Applied Mathematics, Chinese Academy of Science, Beijing, China, 1997. Journal of Optimization Theory and Applications, 103 (1999), forthcoming.