Techniques for accelerating branch-and-bound algorithms dedicated to sparse optimization
Résumé
We propose two acceleration techniques for sparse optimization (the minimization of a cardinality-penalized least-squares function) with branch-and-bound algorithms. Convex duality is applied to the relaxation problems at each node of the search tree, allowing one to early prune suboptimal nodes thanks to the computation of valid dual bounds. Then, screening methods are implemented during each node evaluation, which reduce the problem size by fixing variables to their optimal value. Numerical experiments study the efficiency of such techniques as a function of the problem difficulty.