2021/10/13 by Hui Ouyang, Ouyang, Hui
Computer Science · Mathematics · #47H05 #47J25 #90C30 #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis #Primary 65J15 #Secondary 90C25
paper · pdf · doi:10.48550/arxiv.2110.07015
openalex publication_date 2021/10/13 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal point algorithms for the equivalence of the boundedness of the sequence of iterations generated by this algorithm and the non-emptiness of the zero set of the maximally monotone operator, and for the weak and strong convergence of the algorithm. Our results cover or improve many results on generalized proximal point algorithms in our references. Improvements of our results are illustrated by comparing our results with related known ones.