Best Lipschitz Constants of Solutions of Quadratic Programs

Lucian Coroianu ()
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Lucian Coroianu: University of Oradea

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 3, No 9, 853-875

Abstract: 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.

Keywords: Polyhedron; Quadratic program; Metric projection; Lipschitz continuity; 90C20 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-016-0966-2

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