"Forward-partial inverse-forward splitting for solving monotone inclusions"

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Research areas:
Year:
2015
Type of Publication:
Article
Keywords:
Composite operator, partial inverse, monotone operator theory, splitting algorithms, Tsengs method
Authors:
Journal:
Journal of Optimization Theory and Applications
Volume:
166
Pages:
391-413
ISSN:
022--3239
Abstract:
In this paper, we provide a splitting method for finding a zero of the sum of a maximally monotone operator, a Lipschitzian monotone operator, and a normal cone to a closed vector subspace of a real Hilbert space. The problem is characterised by a simpler monotone inclusion involving only two operators: the partial inverse of the maximally monotone operator with respect to the vector subspace, and a suitable Lipschitzian monotone operator. By applying the Tseng’s method in this context, we obtain a fully split algorithm, that exploits the whole structure of the original problem and generalises partial inverse and Tseng’s methods. Connections with other methods available in the literature are provided, and the flexibility of our setting is illustrated via applications to some inclusions involving m maximally monotone operators, to primal-dual composite monotone inclusions,and to zero-sum games.