BIRS Workshop Lecture Videos
Parallel, Block-Iterative, Primal-Dual Monotone Operator Splitting Combettes, Patrick
We propose new primal-dual decomposition algorithms for solving
systems of inclusions involving sums of linearly composed maximally
monotone operators. At each iteration, only a subset of the monotone
operators needs to be processed, as opposed to all operators as in
established methods. Deterministic strategies are used to select the
blocks of operators activated at each iteration. In addition,
asynchronous implementation is allowed.
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. The novelty of this class of algorithms will be discussed and comparisons with the state of the art will be performed.
Joint work with J. Eckstein.
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