On minimizing the ratio of quadratic functions over an ellipsoid
On minimizing the ratio of quadratic functions over an ellipsoid
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DOI：
10.1080/02331934.2013.840623
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发表时间：
2015-05
期刊：
影响因子：
2.2
通讯作者：
Yong Xia
中科院分区：
文献类型：
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作者：
Yong Xia
我们研究了在可能退化的椭球上最小化两个二次函数之比的优化问题。充分刻画了问题(RQ)的良好定义。我们证明了任何定义良好的(RQ)在没有任何假设的情况下都允许半定规划重构(SDP)。此外，(RQ)的最小值是当且仅当(SDP)有唯一解时。
We study the optimization problem (RQ) of minimizing the ratio of two quadratic functions over a possibly degenerate ellipsoid. The well definition of problem (RQ) is fully characterized. We show any well-defined (RQ) admits a semidefinite programming reformulation (SDP) without any assumption. Moreover, the minimum of (RQ) is attained if and only if (SDP) has a unique solution.