2022/05/13 by Luis M. Briceño-Arias, Briceño-Arias, Luis, F Pérez Roldán +1
Computer Science · Engineering · Mathematics · #47H05 #47H10 #49M29 #65K05 #65K15 #90C25 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Mathematical Programming #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2205.06860
openalex publication_date 2022/05/13 · openalex created_date 2022/05/22 · openalex updated_date 2026/07/28
In this article we provide a splitting method for solving monotone inclusions in a real Hilbert space involving four operators: a maximally monotone, a monotone-Lipschitzian, a cocoercive, and a monotone-continuous operator. The proposed method takes advantage of the intrinsic properties of each operator, generalizing the forward-back-half forward splitting and the Tseng's algorithm with line-search. At each iteration, our algorithm defines the step-size by using a line search in which the monotone-Lipschitzian and the cocoercive operators need only one activation. We also derive a method for solving non-linearly constrained composite convex optimization problems in real Hilbert spaces. Finally, we implement our algorithm in a non-linearly constrained least-square problem, and we compare its performance with available methods in the literature.