Optimization problems involving group sparsity terms

This paper studies a general form problem in which a lower bounded continuously differentiable function is minimized over a block separable set incorporating a group sparsity expression as a constraint or a penalty (or both) in the group sparsity setting. This class of problems is generally hard to...

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Bibliographic Details
Published in:Mathematical programming 2019-11, Vol.178 (1-2), p.39-67
Main Authors: Beck, Amir, Hallak, Nadav
Format: Article
Language:English
Subjects:
Calculus of Variations and Optimal Control
Optimization
Combinatorics
Economic models
Full Length Paper
Graph theory
Mapping
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Optimization
Sparsity
Theoretical
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Summary:This paper studies a general form problem in which a lower bounded continuously differentiable function is minimized over a block separable set incorporating a group sparsity expression as a constraint or a penalty (or both) in the group sparsity setting. This class of problems is generally hard to solve, yet highly applicable in numerous practical settings. Particularly, we study the proximal mapping that includes group-sparsity terms, and derive an efficient method to compute it. Necessary optimality conditions for the problem are devised, and a hierarchy between stationary-based and coordinate-wised based conditions is established. Methods that obtain points satisfying the optimality conditions are presented, analyzed and tested in applications from the fields of investment and graph theory.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-018-1277-1