Heriot-Watt University
Edinburgh EH14 4ASColin Maclaurin Building CMT.19Aa.repetti@hw.ac.uk
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a.repetti@hw.ac.uk
Associate Professor
Department of Actuarial Mathematics and Statistics School of Mathematics and Computer Sciences
Institute of Sensors, Signals, and Systems School of Engineering and Physical Sciences
Department of Actuarial Mathematics and Statistics School of Mathematics and Computer Sciences
Institute of Sensors, Signals, and Systems School of Engineering and Physical Sciences
Convergence Analysis of Block-Coordinate Primal-Dual Algorithms with Arbitrary Random Sampling
Convergence Analysis of Block-Coordinate Primal-Dual Algorithms with Arbitrary Random Sampling
A. Repetti, E. Chouzenoux, et J.-C. Pesquet
ISMP 2015, Pittsburgh, PA, 12-17 Juillet 2015
In many application areas, one must solve minimization problems involving the sum of proper lower-semicontinuous convex functions composed with linear operators. Such problems can be efficiently solved using primal-dual proximal algorithms. When the number of variables is very large, it can be interesting to adopt a block-coordinate strategy in order to limit the occupied memory. In this work, we propose two subclasses of block-coordinate primal-dual algorithms based on the forward-backward iterative scheme. At each iteration, only a subpart of the variables, selected with an arbitrary random rule, is updated. The almost sure convergence of the iterates generated by the algorithms to a solution of the considered problem is proved.
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