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Zbl 1109.90079
Combettes, Patrick L.; Hirstoaga, Sever A.
Equilibrium programming in Hilbert spaces. (English)
[J] J. Nonlinear Convex Anal. 6, No. 1, 117-136 (2005). ISSN 1345-4773; ISSN 1880-5221/e

Given a Hilbert space $\cal{H}$, a closed convex subset $K$ of $\cal{H}$ and a countable family of functions $F_{i}\colon K^2\to R$ ($i\in I$), the authors consider the problem of finding $x\in K$ such that $F_{i}(x,y)\geq0$ for all $i\in I$ and $y\in K$, as well as the problem of finding the projection of $a\in\cal{H}$ 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.
[Constantin Zălinescu (Iaşi) (MR 2006a:90151)]

MSC 2000:: *90C48 Programming in abstract spaces
90C47 Minimax problems
49K27 Optimal control problems in abstract spaces (nec./ suff.)

Cited in: Zbl 1190.47077 Zbl 1170.47044 Zbl 1167.49014 Zbl 1153.49011 Zbl 1152.49009 Zbl 1158.47317 Zbl 1122.47056

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Zentralblatt MATH Berlin [Germany]