In this paper, we study strong convergence of some proximal-type algorithms to a solution of split minimization problem in complete p-uniformly convex metric spaces. We also analyse asymptotic behaviour of the sequence generated by Halpern-type proximal point algorithm and extend it to approximate a common solution of a finite family of minimization problems in the setting of complete p-uniformly convex metric spaces. Furthermore, numerical experiments of our algorithms in comparison with other algorithms are given to show the applicability of our results.
Following recent important results of Moudafi [Journal of Optimization Theory and Applications 150(2011), 275-283] and other related results on variational problems, we introduce a new iterative algorithm for approximating a solution of monotone variational inclusion problem involving multi-valued mapping. The sequence of the algorithm is proved to converge strongly in the setting of Hilbert spaces. As application, we solved split convex optimization problems.
<p>The main purpose of this paper is to introduce a viscosity-type proximal point algorithm, comprising of a nonexpansive mapping and a finite sum of resolvent operators associated with monotone bifunctions. A strong convergence of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a nonexpansive mapping is established in a Hadamard space. We further applied our results to solve some optimization problems in Hadamard spaces.</p>
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