Iterative algorithms with regularization for hierarchical variational inequality problems and convex minimization problems

The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems

and Applied Analysis 3 open topic. For example, it is yet not clear whether the dual approach to (7) of [29] can be extended to the SFP. The original algorithm given in [15] involves the computation of the inverse A (assuming the existence of the inverse of A), and thus has not become popular. A seemingly more popular algorithm that solves the SFP is the CQ algorithm of Byrne [16, 21] which is ...

General Iterative Method for Convex Feasibility Problem via the Hierarchical Generalized Variational Inequality Problems

Let C be a nonempty closed and convex subset of a real Hilbert space H. Let Am, Bm : C → H be relaxed cocoercive mappings for each 1 ≤ m ≤ r, where r ≥ 1 is integer. Let f : C → C be a contraction with coefficient k ∈ (0, 1). Let G : C → C be ξ-strongly monotone and L-Lipschitz continuous mappings. Under the assumption ∩m=1GV I(C,Bm, Am) 6= ∅, where GV I(C,Bm, Am) is the solution set of a gener...

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Random algorithms for convex minimization problems

This paper deals with iterative gradient and subgradient methods with random feasibility steps for solving constrained convex minimization problems, where the constraint set is specified as the intersection of possibly infinitely many constraint sets. Each constraint set is assumed to be given as a level set of a convex but not necessarily differentiable function. The proposed algorithms are ap...