Bundle methods for dual atomic pursuit

Z. Fan, Y. Sun, M. P. Friedlander
53rd Annual Asilomar Conference on Signals, Systems, and Computers (ACSSC), 2019

arXiv

Abstract

The aim of structured optimization is to assemble a solution, using a given set of (possibly uncountably infinite) atoms, to fit a model to data. A two-stage algorithm based on gauge duality and bundle method is proposed. The first stage discovers the optimal atomic support for the primal problem by solving a sequence of approximations of the dual problem using a bundle-type method. The second stage recovers the approximate primal solution using the atoms discovered in the first stage. The overall approach leads to implementable and efficient algorithms for large problems.