A Sequential Quadratic Programming Algorithm Using an Incomplete Solution of the Subproblem

A feature of current sequential quadratic programming SQP methods to solve nonlinear constrained optimization problems is the necessity at each iteration to solve a quadratic program QP. We show that if the QP subproblem is convex and an active-set method is used to solve it, then there exist iterates other than the minimizer that may be used to define a suitable search direction. None of the usual properties of an SQP method are compromised by the new definition of the search direction. We derive some new properties for an SQP method that uses a particular augmented Lagrangian merit function. Specifically we show, under suitable additional assumptions, that the rate of convergence is superlinear. We also show that the penalty parameter used in the merit function is bounded. KR