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In this paper, we propose a catalog of iterative methods for solving the Split Feasibility Problem in the non-convex setting. We study four different optimization formulations of the problem, where each model has advantageous in different settings of the problem. For each model, we study relevant iterative algorithms, some of which are well-known in this area and some are new. All the studied methods, including the well-known CQ Algorithm, are proven to have global convergence guarantees in the non-convex setting under mild conditions on the problems data.
We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that certain over
In this study, we present a general framework of outer approximation algorithms to solve convex vector optimization problems, in which the Pascoletti-Serafini (PS) scalarization is solved iteratively. This scalarization finds the minimum distance fro
This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of infinite dimensional Hilbert spaces. For this purpose, several inertial hybrid and shrinking projection algorithms are proposed under the
We study the robustness of accelerated first-order algorithms to stochastic uncertainties in gradient evaluation. Specifically, for unconstrained, smooth, strongly convex optimization problems, we examine the mean-squared error in the optimization va
We study variational inequalities which are governed by a strongly monotone and Lipschitz continuous operator $F$ over a closed and convex set $S$. We assume that $S=Ccap A^{-1}(Q)$ is the nonempty solution set of a (multiple-set) split convex feasib