An SQP method for mathematical programs with vanishing constraints with strong convergence properties
提出一种求解消失约束数学规划的SQP算法，每步求解带线性消失约束的二次规划，证明迭代点列的所有极限点至少是M-平稳点，扩展后保证更强的Q_M-平稳性。
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.