Amenable cones: error bounds without constraint qualifications
Amenable cones: error bounds without constraint qualifications
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DOI：
10.1007/s10107-019-01439-3
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发表时间：
2017-12
影响因子：
2.7
通讯作者：
Bruno F. Lourenço
中科院分区：
文献类型：
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作者：
Bruno F. Lourenço
我们提供了一个框架，用于获得线性二次曲线问题的误差界，而不需要假设约束限定或正则性条件。我们方法的关键方面是柔顺圆锥和面剩余函数的概念。结果表明，误差界可以表示为面部残差函数的组合。构图的数量与人脸归约技术和问题的奇异性程度有关。特别地，我们证明了对称锥是可服从的，并计算了面部残差函数。由此，我们能够提供一个新的Hölderian误差界，从而推广和揭示了Sturm关于半定矩阵的一个早期结果。我们还给出了可服从锥交的误差界，这将被用来证明双重非负锥的误差界。最后，我们列出了一些有待解决的问题。
We provide a framework for obtaining error bounds for linear conic problems without assuming constraint qualifications or regularity conditions. The key aspects of our approach are the notions ofamenable conesandfacial residual functions. Foramenable cones, it is shown that error bounds can be expressed as a composition of facial residual functions. The number of compositions is related to the facial reduction technique and the singularity degree of the problem. In particular, we show that symmetric cones are amenable and compute facial residual functions. From that, we are able to furnish a new Hölderian error bound, thus extending and shedding new light on an earlier result by Sturm on semidefinite matrices. We also provide error bounds for the intersection of amenable cones, this will be used to prove error bounds for the doubly nonnegative cone. At the end, we list some open problems.