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Sparse Branch and Bound for Exact Optimization of L0-Norm Penalized Least Squares | IEEE Conference Publication | IEEE Xplore

Sparse Branch and Bound for Exact Optimization of L0-Norm Penalized Least Squares


Abstract:

We propose a global optimization approach to solve ℓ0-norm penalized least-squares problems, using a dedicated branch-and-bound methodology. A specific tree search strate...Show More

Abstract:

We propose a global optimization approach to solve ℓ0-norm penalized least-squares problems, using a dedicated branch-and-bound methodology. A specific tree search strategy is built, with branching rules inspired from greedy exploration techniques. We show that the subproblem involved at each node can be evaluated via ℓ1-norm-based optimization problems with box constraints, for which an active-set algorithm is built. Our method is able to solve exactly moderate-size, yet difficult, sparse approximation problems, without resorting to mixed-integer programming (MIP) optimization. In particular, it outperforms the generic MIP solver CPLEX.
Date of Conference: 04-08 May 2020
Date Added to IEEE Xplore: 09 April 2020
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Conference Location: Barcelona, Spain

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