2019/08/16 by Volkan Cevher, Cevher, Volkan, Bằng Công Vũ +1 · 5 citations
Computer Science · Mathematics · #Optimization and Variational Analysis #Contact Mechanics and Variational Inequalities #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1908.05912
The proximal extrapolated gradient method citeMalitsky18a is an extension\nof the projected reflected gradient method citeMalitsky15. Both methods were\nproposed for solving the classic variational inequalities. In this paper, we\ninvestigate the projected reflected gradient method, in the general setting,\nfor solving monotone inclusions involving Lipschitzian operators. As a result,\nwe obtain a simple method for finding a zero point of the sum of two monotone\noperators where one of them is Lipschizian. We also show that one can improve\nthe range of the stepsize of this method for the case when the Lipschitzian\noperator is restricted to be cocoercive. A nice combination of this method and\nthe forward-backward splitting was proposed. As a result, we obtain a new\nsplitting method for finding a zero point of the sum of three operators (\nmaximally monotone + monotone Lipschitzian + cocoercive). Application to\ncomposite monotone inclusions are demonstrated.\n