Switching Stepsize Strategies for SQP

An SQP algorithm is presented for solving constrained nonlinear programming problems. The algorithm uses three stepsize strategies in order to achieve global and superlinear convergence. Switching rules are implemented that combine the merits and avoid the drawbacks of the three stepsize strategies. A penalty parameter is determined using an adaptive strategy that aims to achieve sufficient decrease of the activated merit function. Global convergence is established and it is also shown that, locally, unity step sizes are accepted, and therefore superlinear convergence is not impeded under standard assumptions. Global convergence and convergence of the stepsizes is displayed on test problems from the Hock and Schittkowski collection.