Descent methods for equilibrium problems in a Banach space. (English) Zbl 1057.49009

Summary: We consider equilibrium problems with differentiable bifunctions in a Banach space setting and investigate properties of gap functions for such problems. We suggest a derivative-free descent method and give conditions which provide strong convergence of the method.


49J40 Variational inequalities
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[1] Baiocchi, C.; Capelo, A., Variational and quasivariational inequalities. applications to free boundary problems, (1984), John Wiley and Sons Baltimore, MD · Zbl 0551.49007
[2] Blum, E.; Oettli, W., From optimization and variational inequalities to equilibrium problems, The mathematics student, 63, 127-149, (1994)
[3] Bianchi, M.; Schaible, S., Generalized monotone bifunctions and equilibrium problems, Journal of optimization theory and applications, 90, 31-43, (1996) · Zbl 0903.49006
[4] Konnov, I.V.; Schaible, S., Duality for equilibrium problems under generalized monotonicity, Journal of optimization theory and applications, 104, 395-408, (2000) · Zbl 1016.90066
[5] Blum, E.; Oettli, W., Variational principles for equilibrium problems, (), 79-88 · Zbl 0839.90016
[6] Patriksson, M., Nonlinear programming and variational inequality problems. A unified approach, (1999), Kluwer Frankfurt am Main · Zbl 0913.65058
[7] Wu, J.H.; Florian, M.; Marcotte, P., A general descent framework for the monotone variational inequality problem, Mathematical programming, 61, 281-300, (1993) · Zbl 0813.90111
[8] Konnov, I.V., Combined relaxation methods for variational inequalities, (2000), Springer-Verlag Dordrecht · Zbl 0986.49004
[9] Karmanov, V.G., Mathematical programming, (1986), Nauka Berlin, (in Russian) · Zbl 0349.90075
[10] Dem’yanov, V.F.; Rubinov, A.M., Approximate methods for solving extremum problems, (1968), Leningrad Univ. Press Moscow, English translation, Elsevier, Amsterdam, (1970) · Zbl 0217.46203
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