Abstract
We extend some results of Yen (Math Oper Res 20:695–708, 1995) on the Lipschitz continuity of solutions of quadratic programs. In Yen’s paper only canonical quadratic programs are considered, while in this contribution standard and even general quadratic programs are investigated for two parameters, one appearing in the quadratic function and the other in the right-hand side of the polyhedral constraints. In addition, it is proved that we have a piecewise additive and positively homogenous relation between the parameters and the solution. In particular, we get the same kind of results for the metric projection onto a “moving” polyhedron, as this problem is reduced to the previous one. Noting that in Yen’s paper the Lipschitz constant is not explicitly stated, perhaps the most important improvement is that in every cases we can provide the best (sharpest) Lipschitz constant of the solution function.
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Acknowledgments
I am grateful to the anonymous reviewers for carefully reading the manuscript and for their valuable suggestions, which improved this contribution. This study was supported by a grant from the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, Project No. PN-II-ID-PCE-2011-3-0861.
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Communicated by Alfredo N. Iusem.
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Coroianu, L. Best Lipschitz Constants of Solutions of Quadratic Programs. J Optim Theory Appl 170, 853–875 (2016). https://doi.org/10.1007/s10957-016-0966-2
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DOI: https://doi.org/10.1007/s10957-016-0966-2