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

Matúš Benko () and Helmut Gfrerer ()
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Matúš Benko: Johannes Kepler University Linz
Helmut Gfrerer: Johannes Kepler University Linz

Computational Optimization and Applications, 2017, vol. 67, issue 2, No 5, 399 pages

Abstract: 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 $${\mathcal {Q}}_M$$ 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 $${\mathcal {Q}}_M$$ Q M -stationarity of the limit points.

Keywords: SQP method; Mathematical programs with vanishing constraints; $${\mathcal {Q}}$$ Q -stationarity; $${\mathcal {Q}}_M$$ Q M -stationarity; 49M37; 90C26; 90C55 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-017-9894-9

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