A Stochastic Smoothing Algorithm for Semidefinite Programming

Alexandre d'Aspremont (1, 2) , Noureddine El Karoui (3)

1 LIENS - Laboratoire d'informatique de l'école normale supérieure
2 SIERRA - Statistical Machine Learning and Parsimony
3 Department of Statistics [Berkeley]

We use a rank one Gaussian perturbation to derive a smooth stochastic approximation of the maximum eigenvalue function. We then combine this smoothing result with an optimal smooth stochastic optimization algorithm to produce an efficient method for solving maximum eigenvalue minimization problems. We show that the complexity of this new method is lower than that of deterministic smoothing algorithms in certain precision/dimension regimes.

Domaines: Optimisation et contrôle [math.OC]

Alexandre d'Aspremont, Noureddine El Karoui. A Stochastic Smoothing Algorithm for Semidefinite Programming. SIAM Journal on Optimization, 2014, 24 (3), pp.1138-1177. ⟨hal-00907530⟩