A note on the existence of zeroes of convexly regularized sums of maximal monotone operators |
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Authors: | Regina S. Burachik Susana Scheimberg Paulo J. S. Silva |
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Affiliation: | a Engenharia de Sistemas e Computação, COPPE-UFRJ, CP 68511, CEP 21945-970, Rio de Janeiro, RJ, Brazil;b Computer Science Department, IME-USP, Rua do Matão 1010, CEP 05508-090, São Paulo, SP, Brazil |
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Abstract: | Many algorithms for solving the problem of finding zeroes of a sum of two maximal monotone operators T1 and T2, have regularized subproblems of the kind 0T1(x)+T2(x)+∂D(x), where D is a convex function. We develop an unified analysis for existence of solutions of these subproblems, through the introduction of the concept of convex regularization, which includes several well-known cases in the literature. Finally, we establish conditions, either on D or on the operators, which assure solvability of the subproblems. |
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Keywords: | Zeros of sums of maximal monotone operators Legendre functions Generalized proximal-like algorithms Regularization |
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