2013/06/03 by Radu Ioan Boţ, Bot, Radu Ioan, Ernö Robert Csetnek +1 · 2 citations
Computer Science · Medicine · #47H05 #65K05 #90C25 #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Functional Analysis (math.FA) #Hip disorders and treatments #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1306.0352
openalex publication_date 2013/06/03 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We deal with monotone inclusion problems of the form 0\∈ Ax+Dx+NC(x) in\nreal Hilbert spaces, where A is a maximally monotone operator, D a\ncocoercive operator and C the nonempty set of zeros of another cocoercive\noperator. We propose a forward-backward penalty algorithm for solving this\nproblem which extends the one proposed by H. Attouch, M.-O. Czarnecki and J.\nPeypouquet in [3]. The condition which guarantees the weak ergodic convergence\nof the sequence of iterates generated by the proposed scheme is formulated by\nmeans of the Fitzpatrick function associated to the maximally monotone operator\nthat describes the set C. In the second part we introduce a\nforward-backward-forward algorithm for monotone inclusion problems having the\nsame structure, but this time by replacing the cocoercivity hypotheses with\nLipschitz continuity conditions. The latter penalty type algorithm opens the\ngate to handle monotone inclusion problems with more complicated structures,\nfor instance, involving compositions of maximally monotone operators with\nlinear continuous ones.\n