An SQP method for mathematical programs with vanishing constraints with strong convergence properties

Abstract

We propose an SQP algorithm for mathematical programs with vanishing constraints which solves at each iteration a quadratic program with linear vanishing constraints. The algorithm is based on the newly developed concept of $\mathcal{Q}$-stationarity [5]. We demonstrate how ${\mathcal{Q}}_M$-stationary solutions of the quadratic program can be obtained. We show that all limit points of the sequence of iterates generated by the basic SQP method are at least M-stationary and by some extension of the method we also guarantee the stronger property of ${\mathcal{Q}}_M$-stationarity of the limit points.