Finding a zero of the sum of two maximal monotone operators. (English) Zbl 0891.49005

Summary: The equivalence between variational inclusions and a generalized type of Wiener-Hopf equation is established. This equivalence is then used to suggest and analyze iterative methods in order to find a zero of the sum of two maximal monotone operators. Special attention is given to the case where one of the operators is Lipschitz continuous and either is strongly monotone or satisfies the Dunn property. Moreover, when the problem has a nonempty solution set, a fixed-point procedure is proposed and its convergence is established provided that the Brézis-Crandall-Pasy condition holds true. More precisely, it is shown that this allows reaching the element of minimal norm of the solution set.


49J40 Variational inequalities
47H05 Monotone operators and generalizations
47J20 Variational and other types of inequalities involving nonlinear operators (general)
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
49M27 Decomposition methods
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