Séminaire Analyse-Proba (Guillaume Olikier, mardi 14 novembre)

Le prochain séminaire Analyse-Proba aura lieu mardi 14 novembre à 10h30 en salle A711. Guillaume OLIKIER (Inria - Université Côte d'Azur) nous parlera de "First-order optimization on stratified sets".

Title : First-order optimization on stratified sets

Abstract 
This talk considers the problem of minimizing a differentiable function with locally Lipschitz continuous gradient on a stratified set (i.e., a set that can be partitioned into finitely many smooth manifolds), and presents two first-order algorithms, called P²GDR and RFDR, guaranteed to accumulate at stationary points of this problem under suitable assumptions on the stratified set. These algorithms are based respectively on the projected-projected gradient descent (P²GD) method and the retraction-free descent (RFD) method both introduced by Schneider and Uschmajew (2015). Examples of sets satisfying the assumptions required by P²GDR include the determinantal variety (i.e., matrices of bounded rank), its intersection with the cone of positive-semidefinite matrices, the set of sparse vectors, and the set of nonnegative sparse vectors. Examples of sets satisfying the assumptions required by RFDR include the determinantal variety and the set of sparse vectors. P²GDR and RFDR are the only first-order algorithms known to accumulate at stationary points of the considered problem under assumptions satisfied by the determinantal variety.