Branch-and-bound algorithm applied to sparse optimization problems: a study of some exploration strategies
Abstract
Sparse optimization focuses on finding a solution to least-squares problems with few non-zero components. Applications include inverse problems in signal processing, subset selection, or portfolio optimization. Optimization problems can be formulated as mixed-integer programs. A dedicated branchand-bound algorithm is able to exploit the specific structure of such problems and finds the global minimum much faster than generic MIP solvers. We will present some results about the fine-tuning process of this branch-and-bound algorithm, focusing mainly on the exploration strategy.