ON A NEW GENERALIZED REGULARIZATION METHOD IN THE TIKHONOV SENSE FOR SADDLE FUNCTIONS AND APPLICATION TO VARIATIONAL ASYMPTOTIC DEVELOPMENTS AND MINIMAX PROBLEMS
Ibn Tofail University, Faculty of Sciences of KÚnitra, Laboratory of NonLinear Analysis,Cryptography, Informatic, Operations Research and Statistics.
Department of Mathematics BP.133, KÚnitra, Morocco.
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In this paper we introduce a wide class of generalized regularization methods in the Tikhonov sense for saddle point theory and minimax problems in a general Hausdorff topological space. First we prove a central theorem (Th.2.1) from which we derive various types of approximation results and variational asymptotic developments. An application is given to the conjugacy for bivariate functions defined on a normed space. Well-posedness of such regularizations is also investigated when the functions under consideration are convex-concave, semicontinuous and defined on the product of two reflexive Banach spaces. A stability result involving a class of variational convergences of operators has been also displayed within the framework of variational asymptotic developments.
Key words and phrases: Generalized regularization method in the Tikhonov sense for bivariate functions, saddle point and minimax problem, variational asymptotic developments, conjugacy, stability and sensitivity analysis, well-posedness, epi/hypo-convergence.
2010 MSC. Primary: 49K40; Secondary: 49J35, 49K35, 49J52, 90C47, 90C31.
The results of this paper were presented at a National Conference on NonLinear Analysis and Geometry held at Agadir Morocco, in June 2014.
eJournal of Mathematical Sciences, Technology and Humanities
Issue 3, Pages: 1317 - 1330