A Dykstra-like algorithm for two monotone operators

By Heinz H. Bauschkeand, Patrick L. Combettes. 2007

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View Paper: https://www.semanticscholar.org/paper/486c479e51304bff00bfbfee22fc1be04c10a66a

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Citations in the corpus

Group Regularized Estimation Under Structural Hierarchy (2014, background): “2;( + > )=2). Similarly, the globally optimal solution to min =[b; ]> 1 2 k 0k2 F + k( 1>) >k 2;1 is given by o with o[;;k] = ~ S( 0[:;k]; [k]), 1 kp. Applying Theorem 3.2 and 3.3 in Bauschke and Combettes (2008) guarantees the strict convergence of the iterates and the global optimalit”
Proximity for sums of composite functions (2010, background): “22), see [3] for the case when m = 2, and [5] for the case of best approximation).”
Entropic Approximation of Wasserstein Gradient Flows (2015, background): “Note that such an extension is well known for the case of the L2 metric [7].”
Iterative Bregman Projections for Regularized Transportation Problems (2014, background): “Note that several other proximal algorithms have been extended to this setting [5].”
Proximal Splitting Methods in Signal Processing (2009, methodology): “3 [12] Every sequence (xn)n∈N generated by Algorithm1.”
Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization (2011, methodology): “uickly compute an approximate proximity operator using the block coordinate descent (BCD) algorithm presented in [12], which is equivalent to the proximal variant of Dykstra’s algorithm introduced by [34]. In our implementation of the BCD method, we alternate between computing the proximity operator”
Proximal Splitting Algorithms: A Tour of Recent Advances, with New Twists. (2020, methodology): “This selected overview of proximal splitting methods is by no way exhaustive; for instance, we did not cover the forward–backward–forward splitting method and its applications [27,91,97] [25, section 26.6], or Dykstra-like algorithms [98, 99] [25, section 30.2].”