Auxiliary principle and iterative algorithm for a new system of generalized mixed equilibrium problems in Banach spaces. (English) Zbl 1259.65082
Mixed variational-like inequalities is an important and useful generalization of variational inequalities having significant applications in nonconvex optimization. A new system of generalized mixed equilibrium problems
involving skew-symmetric bifunctions (SGMEP) is studied in reflexive Banach spaces. The skew-symmetric bifunctions have the properties which can be considered as analogs of monotonicity of gradient and nonnegativity of the second derivative for a convex function. A system of auxiliary mixed equilibrium problems (SAMEP) is proposed for solving the SGMEP and the existence and uniqueness of the solutions of the SAMEP are proved. For computing the approximate solutions of the SGMEP a new iterative algorithm based on the auxiliary principle technique is developed and analyzed. The strong convergence of the sequences generated by the algorithm is also proved under quite mild conditions.
Reviewer: Otu Vaarmann (Tallinn)
MSC:
| 65J15 | Numerical solutions to equations with nonlinear operators |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 47J25 | Iterative procedures involving nonlinear operators |
Keywords:
system of generalized mixed equilibrium problems involving skew-symmetric bifunctions; auxiliary principle; iterative algorithm; reflexive Banach space; mixed variational-like inequalities; nonconvex optimization; convergenceReferences:
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