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• W2000311910 abstract "Let C be a nonempty closed convex subset of a real Hilbert space H. Let f:C→H be a ρ-contraction. Let S:C→C be a nonexpansive mapping. Let B,B˜:H→H be two strongly positive bounded linear operators. Consider the triple-hierarchical constrained optimization problem of finding a point x∗ such that x∗∈Ω,〈(B˜−γf)x∗−(I−B)Sx∗,x−x∗〉≥0,∀x∈Ω, where Ω is the set of the solutions of the following variational inequality: x∗∈EP(F,A),〈(B˜−S)x∗,x−x∗〉≥0,∀x∈EP(F,A), where EP(F,A) is the set of the solutions of the equilibrium problem of finding z∈C such that F(z,y)+〈Az,y−z〉≥0,∀y∈C. Assume Ω≠0̸. The purpose of this paper is the solving of the above triple-hierarchical constrained optimization problem. For this purpose, we first introduce an implicit double-net algorithm. Consequently, we prove that our algorithm converges hierarchically to some element in EP(F,A) which solves the above triple-hierarchical constrained optimization problem. As a special case, we can find the minimum norm x∗∈EP(F,A) which solves the monotone variational inequality 〈(I−S)x∗,x−x∗〉≥0,∀x∈EP(F,A)." @default.
• W2000311910 created "2016-06-24" @default.
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• W2000311910 date "2012-02-01" @default.
• W2000311910 modified "2023-09-23" @default.
• W2000311910 title "A unified implicit algorithm for solving the triple-hierarchical constrained optimization problem" @default.
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• W2000311910 doi "https://doi.org/10.1016/j.mcm.2011.10.041" @default.
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