Iteration Complexity of a Fixed-Stepsize SQP Method for Nonconvex Optimization with Convex Constraints

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.