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Variational inequalities, complementarity problems, and duality theorems. (English) Zbl 0383.49005


MSC:

49J40 Variational inequalities
49J35 Existence of solutions for minimax problems
49J45 Methods involving semicontinuity and convergence; relaxation
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[1] Bourbaki, N., Espaces Vectoriels Topologiques (1967), Hermann: Hermann Paris, Chap. 3, 4, and 5 · Zbl 0066.35301
[2] Brézis, H.; Nirenberg, L.; Stampacchia, G., A remark on Ky Fan’s minimax principle, Boll. Un. Mat. Ital., 6, 293-300 (1972) · Zbl 0264.49013
[3] Fan, K., A generalization of the Alaoglu-Bourbaki theorem and its applications, Math. Z., 88, 48-60 (1965) · Zbl 0135.34402
[4] Fan, K., A minimax inequality and applications, (Shisha, O., Inequalities III (1972), Academic Press: Academic Press New York/London) · Zbl 0302.49019
[5] Karamardian, S., The generalized complementarity problem, J. Optimization Theory Appl., 8, 161-168 (1971) · Zbl 0218.90052
[6] S. Karamardian; S. Karamardian · Zbl 0304.49026
[7] Köthe, G., Topological Vector Spaces (1969), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York
[8] Lemke, C. E., Recent results on complementarity problems, (Rosen, J. B.; Mangasarian, O. L.; Ritter, K., Nonlinear Programming (1970), Academic Press: Academic Press New York/London) · Zbl 0227.90043
[9] Moré, J. J., Classes of functions and feasibility conditions in nonlinear complementarity problems, Cornell University Technical Reports 73-174 (1973), Ithaca, N. Y. · Zbl 0291.90059
[10] Moreau, J. J., Sur la fonction polaire d’une fonction semicontinue supérieurement, C. R. Acad. Sci. Paris, 258, 1128-1130 (1964) · Zbl 0144.30501
[11] Moreau, J. J., Fonctionelles convexes, (Séminaire sur les Équations aux Dérivées Partielles. Séminaire sur les Équations aux Dérivées Partielles, Lecture notes (1966), Collège de France) · Zbl 0343.49021
[12] Rockafellar, R. T., Duality and stability in extremum problems involving convex functions, Pacific J. Math., 21, 167-187 (1967) · Zbl 0154.44902
[13] Stampacchia, G., Variational inequalities, (Ghizzetti, A., Theory and Application of Monotone Operators (1969), Edizioni Oderisi: Edizioni Oderisi Gubbio, Italy) · Zbl 0152.34601
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