Asynchronous block-iterative primal-dual decomposition methods for monotone inclusions

We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the sense that, at each iteration, only a subset of the monotone op...

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Vydáno v:	Mathematical programming Ročník 168; číslo 1-2; s. 645 - 672
Hlavní autoři:	Combettes, Patrick L., Eckstein, Jonathan
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2018 Springer Nature B.V
Témata:	Algorithms Calculus of Variations and Optimal Control; Optimization Combinatorics Convergence Decomposition Full Length Paper Half spaces Inclusions Innovations Linear operators Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Theoretical Monotone inclusion Primal-dual algorithm 65K05 90C25 Splitting algorithm Duality Monotone operator 49M27 Block-iterative algorithm Asynchronous algorithm 47H05
ISSN:	0025-5610, 1436-4646
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Shrnutí:	We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the sense that, at each iteration, only a subset of the monotone operators needs to be processed, as opposed to all operators as in established methods. Flexible strategies are used to select the blocks of operators activated at each iteration. In addition, we allow lags in operator processing, permitting asynchronous implementation. The decomposition phase of each iteration of our methods is to generate points in the graphs of the selected monotone operators, in order to construct a half-space containing the Kuhn–Tucker set associated with the system. The coordination phase of each iteration involves a projection onto this half-space. We present two related methods: the first method provides weakly convergent primal and dual sequences under general conditions, while the second is a variant in which strong convergence is guaranteed without additional assumptions. Neither algorithm requires prior knowledge of bounds on the linear operators involved or the inversion of linear operators. Our algorithmic framework unifies and significantly extends the approaches taken in earlier work on primal-dual projective splitting methods.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0025-5610 1436-4646
DOI:	10.1007/s10107-016-1044-0