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

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 [Formula: see text] -stationarity (Benko and Gfrerer in Optimization 66(1):6...

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Detalles Bibliográficos
Autores principales: Benko, Matúš, Gfrerer, Helmut
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2017
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5397537/
https://www.ncbi.nlm.nih.gov/pubmed/28479672
http://dx.doi.org/10.1007/s10589-017-9894-9
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author Benko, Matúš
Gfrerer, Helmut
author_facet Benko, Matúš
Gfrerer, Helmut
author_sort Benko, Matúš
collection PubMed
description 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 [Formula: see text] -stationarity (Benko and Gfrerer in Optimization 66(1):61–92, 2017). We demonstrate how [Formula: see text] -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 [Formula: see text] -stationarity of the limit points.
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spelling pubmed-53975372017-05-05 An SQP method for mathematical programs with vanishing constraints with strong convergence properties Benko, Matúš Gfrerer, Helmut Comput Optim Appl Article 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 [Formula: see text] -stationarity (Benko and Gfrerer in Optimization 66(1):61–92, 2017). We demonstrate how [Formula: see text] -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 [Formula: see text] -stationarity of the limit points. Springer US 2017-02-06 2017 /pmc/articles/PMC5397537/ /pubmed/28479672 http://dx.doi.org/10.1007/s10589-017-9894-9 Text en © The Author(s) 2017 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Benko, Matúš
Gfrerer, Helmut
An SQP method for mathematical programs with vanishing constraints with strong convergence properties
title An SQP method for mathematical programs with vanishing constraints with strong convergence properties
title_full An SQP method for mathematical programs with vanishing constraints with strong convergence properties
title_fullStr An SQP method for mathematical programs with vanishing constraints with strong convergence properties
title_full_unstemmed An SQP method for mathematical programs with vanishing constraints with strong convergence properties
title_short An SQP method for mathematical programs with vanishing constraints with strong convergence properties
title_sort sqp method for mathematical programs with vanishing constraints with strong convergence properties
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5397537/
https://www.ncbi.nlm.nih.gov/pubmed/28479672
http://dx.doi.org/10.1007/s10589-017-9894-9
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