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Algorithms of common solutions for generalized mixed equilibria, variational inclusions, and constrained convex minimization. (English) Zbl 1470.49017

Summary: We introduce new implicit and explicit iterative algorithms for finding a common element of the set of solutions of the minimization problem for a convex and continuously Fréchet differentiable functional, the set of solutions of a finite family of generalized mixed equilibrium problems, and the set of solutions of a finite family of variational inclusions in a real Hilbert space. Under suitable control conditions, we prove that the sequences generated by the proposed algorithms converge strongly to a common element of three sets, which is the unique solution of a variational inequality defined over the intersection of three sets.

MSC:

49J40 Variational inequalities
47J25 Iterative procedures involving nonlinear operators
90C25 Convex programming
90C48 Programming in abstract spaces
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