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Best Lipschitz Constants of Solutions of Quadratic Programs

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  • Lucian Coroianu

    (University of Oradea)

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.

Suggested Citation

  • Lucian Coroianu, 2016. "Best Lipschitz Constants of Solutions of Quadratic Programs," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 853-875, September.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:3:d:10.1007_s10957-016-0966-2
    DOI: 10.1007/s10957-016-0966-2
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    References listed on IDEAS

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    1. Shu Lu & Stephen M. Robinson, 2008. "Variational Inequalities over Perturbed Polyhedral Convex Sets," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 689-711, August.
    2. N. D. Yen, 1995. "Lipschitz Continuity of Solutions of Variational Inequalities with a Parametric Polyhedral Constraint," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 695-708, August.
    3. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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