Dipartimento di Ingegneria informatica, automatica e gestionale

We consider an SQP method for solving nonconvex optimization problems whose feasible set is convex and with an objective function that is the sum of a smooth nonconvex term and a nonsmooth, convex one. In the proposed method, at each iteration, a direction is generated by solving a strongly convex approximation to the original problem and then a fixed-stepsize is taken in that direction. The complexity result we establish is, as far as we are aware, the best available for the rather general setting we consider.