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

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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… Click to show full 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 $${\mathcal {Q}}$$Q-stationarity (Benko and Gfrerer in Optimization 66(1):61–92, 2017). We demonstrate how $${\mathcal {Q}}_M$$QM-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 $${\mathcal {Q}}_M$$QM-stationarity of the limit points.

Keywords: mathematical programs; method mathematical; constraints strong; sqp method; programs vanishing; vanishing constraints

Journal Title: Computational Optimization and Applications
Year Published: 2017

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