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.

中文翻译：

---

一种用于数学程序的SQP方法，具有消失的约束和强大的收敛性。

我们为具有消失约束的数学程序提出了一种SQP算法，该算法在每次迭代时求解具有线性消失约束的二次程序。该算法基于新开发的\（{\ mathcal {Q}} \） -平稳性（Benko和Gfrerer in Optimization 66（1）：61–92，2017）。我们演示了如何获得二次程序的\（{\ mathcal {Q}} _ M \） -平稳解。我们显示了基本SQP方法生成的迭代序列的所有极限点至少是M平稳的，并且通过对该方法的某些扩展，我们还保证了\（{\ mathcal {Q}} _ M \）的更强属性-极限点的平稳性。