Vendredi 18 Novembre
Heure: 
10:30  11:30 
Lieu: 
Amphi Copernic 
Résumé: 
On the solution of convex SemiInfinite Problems 
Description: 
Martina Cerulli In this talk, we will present the results of the paper "Convergent algorithms for a class of convex semiinfinite programs" by M. Cerulli, A. Oustry, C. D'Ambrosio, L. Liberti, accepted for publication on SIAM Journal on Optimization. In this paper, we focus on convex SemiInfinite Problems (SIPs) with an infinite number of quadratically parametrized constraints, not necessarily convex w.r.t. the parameter. A new convergent approach to solve these SIPs is proposed, leveraging the dualization of the inner problem. Indeed, based on the Lagrangian dual of the inner problem, a convex and tractable restriction of the considered SIP is derived. We state sufficient conditions for the optimality of this restriction. If these conditions are not met, the restriction is enlarged through an InnerOuter Approximation Algorithm, and its value converges to the value of the original semiinfinite problem. This new algorithmic approach is compared with the classical Cutting Plane algorithm. We propose a new rate of convergence of the Cutting Plane algorithm, directly related to the iteration index, derived when the objective function is strongly convex, and under a strict feasibility assumption. We successfully test the two methods on two applications: the constrained quadratic regression and a zerosum game with cubic payoff. 

