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

TL;DR

This paper introduces a sequential quadratic programming (SQP) method tailored for mathematical programs with vanishing constraints, ensuring strong convergence to stationary solutions by leveraging the concept of $\\mathcal Q$-stationarity.

Contribution

The paper develops a novel SQP algorithm that guarantees convergence to $\\mathcal Q_M$-stationary solutions in problems with vanishing constraints, advancing solution stability.

Findings

All limit points are at least M-stationary.

Extended method guarantees $\\mathcal Q_M$-stationarity of limit points.

The algorithm effectively handles quadratic programs with linear vanishing constraints.

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.