A Sequential Quadratic Programming Method Without A Penalty Function or a Filter for Nonlinear Equality Constrained Optimization

Abstract

We present a sequential quadratic programming method without using a penalty function or a filter for solving nonlinear equality constrained optimization. In each iteration, the linearized constraints of the quadratic programming are relaxed to satisfy two mild conditions; the step-size is selected such that either the value of the objective function or the measure of the constraint violations is sufficiently reduced. As a result, our method has two nice properties. First, we do not need to assume the boundedness of the iterative sequence. Second, we do not need any restoration phase which is necessary for filter methods. We prove that the algorithm will terminate at either an approximate Karush–Kuhn–Tucker point, an approximate Fritz–John point, or an approximate infeasible stationary point which is an approximate stationary point for minimizing the l2 norm of the constraint violations. By controlling the exactness of the linearized constraints and introducing a second-order correction technique, without...