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Mixed equilibrium problems: sensitivity analysis and algorithmic aspect. (English) Zbl 1103.49301

Summary: The aim of this paper is twofold. First, it is to extend the sensitivity analysis framework, developed recently for variational inequalities, to mixed equilibrium problems. The second is to propose iterative methods for solving this kind of problems. In the process, we establish an equivalence between an extended version of Wiener-Hopf equations and the given problems relying on a generalization of the Yosida approximation notion. Our results generalize results obtained for optimization, variational inequalities, complementarity problems, and problems of Nash equilibria.

MSC:

49J40 Variational inequalities
90C31 Sensitivity, stability, parametric optimization
47J20 Variational and other types of inequalities involving nonlinear operators (general)
65J15 Numerical solutions to equations with nonlinear operators
90C47 Minimax problems in mathematical programming
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