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NODE-SCREENING TESTS FOR THE L0-PENALIZED LEAST-SQUARES PROBLEM

Citation Author(s):
Theo Guyard, Cedric Herzet, Clement Elvira
Submitted by:
Theo Guyard
Last updated:
5 May 2022 - 2:27am
Document Type:
Presentation Slides
Document Year:
2022
Event:
Presenters:
Theo Guyard
Paper Code:
SPTM-2.5
 

We present a novel screening methodology to safely discard irrelevant nodes within a generic branch-and-bound (BnB) algorithm solving the l0-penalized least-squares problem. Our contribution is a set of two simple tests to detect sets of feasible vectors that cannot yield optimal solutions. This allows to prune nodes of the BnB search tree, thus reducing the overall optimization time. One cornerstone of our contribution is a nesting property between tests at different nodes that allows to implement them with a low computational cost. Our work leverages the concept of safe screening, well known for sparsity-inducing convex problems, and some recent advances in this field for l0-penalized regression problems.

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