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

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 (Benko and Gfrerer in Optimization 66(1):61–92, 2017). 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.