6 research outputs found
ITERATIVE COMPUTATION FOR SOLVING CONVEX OPTIMIZATION PROBLEMS OVER THE SET OF COMMON FIXED POINTS OF QUASI-NONEXPANSIVE AND DEMICONTRACTIVE MAPPINGS
In this paper, a new iterative method for solving convex minimization problems over the set of common fixed points of quasi-nonexpansive and demicontractive mappings is constructed. Convergence theorems are also proved in Hilbert spaces without any compactness assumption. As an application, we shall utilize our results to solve quadratic optimization problems involving bounded linear operator. Our theorems are significant improvements on several important recent results
Contraction-mapping algorithm for the equilibrium problem over the fixed point set of a nonexpansive semigroup
In this paper, we consider the proximal mapping of a bifunction. Under the Lipschitz-type and the strong monotonicity conditions, we prove that the proximal mapping is contractive. Based on this result, we construct an iterative process for solving the equilibrium problem over the fixed point sets of a nonexpansive semigroup and prove a weak convergence theorem for this algorithm. Also, some preliminary numerical experiments and comparisons are presented.
First Published Online: 21 Nov 201