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Strong convergence for an iterative method for the triple-hierarchical constrained optimization problem. (English) Zbl 1238.65061
Summary: The variational inequality problem for a monotone operator over the fixed point set of a nonexpansive mapping is connected with many signal processing problems, and such problems have hierarchical structure, for example, the convex optimization problem over the solution set of the variational inequality problem over the fixed point set has triple-hierarchical structure. In this paper, we present an iterative algorithm for this problem. The strong convergence for the proposed algorithm to the solution is guaranteed under some assumptions.

MSC:
65K15Numerical methods for variational inequalities and related problems
47N10Applications of operator theory in optimization, convex analysis, programming, economics
49J40Variational methods including variational inequalities
47J25Iterative procedures (nonlinear operator equations)
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)