Best Lipschitz Constants of Solutions of Quadratic Programs
Best Lipschitz Constants of Solutions of Quadratic Programs
复制标题
二次规划解的最佳Lipschitz常数
DOI：
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发表时间：
2016
影响因子：
1.9
通讯作者：
Lucian C. Coroianu
中科院分区：
文献类型：
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作者：
Lucian C. Coroianu
我们扩展了 Yen (Math Oper Res 20:695–708, 1995) 关于二次规划解的 Lipschitz 连续性的一些结果。 Yen 的论文只考虑了规范二次规划，而在这个贡献标准中，甚至一般二次规划都针对两个参数进行了研究，一个出现在二次函数中，另一个出现在多面体约束的右侧。此外，还证明了参数与解之间存在分段可加且正齐次的关系。特别是，对于“移动”多面体的度量投影，我们得到了相同的结果，因为这个问题被简化为前一个问题。注意到 Yen 的论文中没有明确说明 Lipschitz 常数，也许最重要的改进是在每种情况下我们都可以提供解函数的最佳（最锐利）Lipschitz 常数。
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.