Randomized First-Order algorithms for bilinear saddle point problems and their applications to l1 minimization
Résumé
In this talk, we propose randomized first-order algorithms for solving bilinear saddle points problems. Our developments are motivated by the need for sublinear time algorithms to solve large-scale parametric bilinear saddle point problems where cheap online assessment of solution quality is crucial. We present the theoretical efficiency estimates of our algorithms and discuss a number of applications, primarily to the problems of l1 minimization arising in sparsity-oriented Signal Processing. We demonstrate, both theoretically and by numerical examples, that when seeking for medium-accuracy solutions of large-scale l1 minimization problems, our randomized algorithms outperform significantly (and progressively as the sizes of the problems grow) the state-of-the-art deterministic methods.