Sequential randomized algorithms for sampled convex optimization

Motivated by the complexity of solving convex scenario problems in one-shot, two new algorithms for the sequential solution of sampled convex optimization problems are presented, for full constraint satisfaction, partial constraint satisfaction, respectively. A rigorous analysis of the theoretical properties of the algorithms is provided,, the related sample complexity is derived. Extensive numerical simulations for a non-trivial example testify the goodness of the proposed solution.