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An SQP method for mathematical programs with vanishing constraints with strong convergence properties. (English) Zbl 1406.90094

Summary: 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 [M. Benko and H. Gfrerer, Optimization 66, No. 1, 61–92 (2017; Zbl 1394.90526)]. 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.

MSC:

90C26 Nonconvex programming, global optimization
90C55 Methods of successive quadratic programming type
49M37 Numerical methods based on nonlinear programming

Citations:

Zbl 1394.90526
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References:

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