Efficient Serial and Parallel Coordinate Descent Methods for Huge-Scale Truss Topology Design

By Peter Richtárik, Martin Takác. 2011

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Distributed Coordinate Descent Method for Learning with Big Data (2013, methodology): “These approaches can be combined, and theory was developed for methods that update a random subset of blocks of coordinates at a time (Richt´arik & Tak´aˇc, 2012a; Fercoq & Richt´arik, 2013).”
Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function (2011, background): “sensing [8], regression [27], protein loop closure [2] and t russ topology design [16]—partly due to a change in the sizeandnature of datadescribed above.”
Parallel coordinate descent methods for big data optimization (2012, methodology): “In Section 2.2 we propose two parallel block coordinate descent methods and comment in some detail on the steps.”
Distributed Block Coordinate Descent for Minimizing Partially Separable Functions (2014, unknown): “cyclic ([27]), greedy ([21]), or randomized.”
Coordinate descent with arbitrary sampling I: algorithms and complexity† (2014, methodology): “After the seminal work of Nesterov [24], which provided an early theoretical justification of these methods for unconstrained convex minimization, the study has been successively extended to L1-regularized [28,34], proximal [17,30], parallel [6,32], distributed [7,26,29] and primal-dual [26,38] vari”
On the Convergence of Block Coordinate Descent Type Methods (2013, background): “The authors also demonstrated in [16] the ability of various block coordinate decent methods to solve large-scale truss topology design problems.”
Separable approximations and decomposition methods for the augmented Lagrangian (2013, unknown): “The methods are used in a number of applications, including linear classification [5, 15, 41], compressed sensing [17], truss topology design [28], solving linear systems of equations [16] and group lasso problems [27].”
Inexact Coordinate Descent: Complexity and Preconditioning (2013, background): “Traditionally cyclic schemes [32] and greedy schemes [28] were studied.”
On optimal probabilities in stochastic coordinate descent methods (2013, methodology): “methods were considered in [2,19,21], and more recently in [1,5,6,12,13,25,27,28].”