MULTI-STEP INERTIAL PROXIMAL POINT ALGORITHM FOR THE SPLIT COMMON SOLUTION PROBLEM OF MONOTONE OPERATOR EQUATIONS

Tóm tắt

The split feasibility problem plays an important role in various fields such as optimization theory, signal processing, image reconstruction, game theory, and several other areas. Based on the proximal point method combined with a multi-step inertial term, the author proposes a new algorithm to solve a generalized form of the split feasibility problem. Specifically, this paper introduces a multi-step inertial proximal point algorithm to solve the split common solution problem for monotone operator equations with multiple out- put sets in real Hilbert spaces. Under suitable conditions on the control parameters, the sequence generated by the proposed algorithm converges weakly to a solution of the problem. Additionally, the paper presents the applicability of the proposed algorithm to related problems such as the split common fixed point problem, the split feasibility problem, and the split common null point problem with multiple output sets, thereby demonstrating the effectiveness and potential extensibility of the proposed algorithm.