Techniques for accelerating branch-and-bound algorithms dedicated to sparse optimization

Techniques for accelerating branch-and-bound algorithms dedicated to sparse optimization

Sparse optimization-fitting data with a low-cardinality linear model-is addressed through the minimization of a cardinality-penalized least-squares function, for which dedicated branch-and-bound algorithms clearly outperform generic mixed-integer-programming solvers. Three acceleration techniques ar...

Full description

Saved in:
Bibliographic Details
Published in:Optimization methods & software Vol. 39; no. 1; pp. 4 - 41
Main Authors: Samain, Gwenaël, Bourguignon, Sébastien, Ninin, Jordan
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02-01-2024
Taylor & Francis Ltd
Subjects:
Algorithms
Branch-and-bound
cardinality
Computer Science
convex relaxation
duality
exploration strategy
Least squares
Mixed integer
Nodes
Operations Research
Optimization
Signal and Image Processing
Solvers
exploration strategy
convex relaxation
branch-and-bound
duality
cardinality
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Sparse optimization-fitting data with a low-cardinality linear model-is addressed through the minimization of a cardinality-penalized least-squares function, for which dedicated branch-and-bound algorithms clearly outperform generic mixed-integer-programming solvers. Three acceleration techniques are proposed for such algorithms. Convex relaxation problems at each node are addressed with dual approaches, which can early prune suboptimal nodes. Screening methods are implemented, which fix variables to their optimal value during the node evaluation, reducing the subproblem size. Numerical experiments show that the efficiency of such techniques depends on the node cardinality and on the structure of the problem matrix. Last, different exploration strategies are proposed to schedule the nodes. Best-first search is shown to outperform the standard depth-first search used in the related literature. A new strategy is proposed which first explores the nodes with the lowest least-squares value, which is shown to be the best at finding the optimal solution-without proving its optimality. A C++ solver with compiling and usage instructions is made available. 
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2023.2241154