A NEW CONVERGENCE ANALYSIS FOR MINIMUM NORM SOLUTION OF SPLIT SYSTEM OF NONSMOOTH MINIMIZATION PROBLEMS

Abstract

This work presents a novel self-adaptive steepest-descent type algorithm for solving the split system of minimization problem (SSMP) related to convex nonsmooth functions. The algorithm includes a self-adaptive step size mechanism, which uses a step size that does not need prior information about the operator norm. Under certain weakened assumptions of parameters, a strong convergence theorem is established and proved for the algorithm. Specifically, the sequence generated by this new algorithm strongly converges towards the minimum norm element of the SSPM. To assess the implementation of our algorithm, a numerical example is provided. According to the numerical results, our algorithm showcases effectiveness and simplicity in its implementation. Furthermore, the primary numerical experiment results indicate that our proposed algorithm surpasses some existing results in the literature in terms of CPU time and iteration count. Our result represents an extension and enhancement of recent findings in this area.