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Equilibrium programming in Hilbert spaces. (English) Zbl 1109.90079
Given a Hilbert space , a closed convex subset K of and a countable family of functions F i :K 2 R (iI), the authors consider the problem of finding xK such that F i (x,y)0 for all iI and yK, as well as the problem of finding the projection of a on S, the solution set of the preceding problem. In order to accomplish these aims, proximal-like block-iterative algorithms, as well as regularization and splitting algorithms, are proposed. For every algorithm, convergence results are established.

MSC:
90C48Programming in abstract spaces
90C47Minimax problems
49K27Optimal control problems in abstract spaces (optimality conditions)