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arXiv · 1611.08781

On the {\L}ojasiewicz Exponent of the Quadratic Sphere Constrained Optimization Problem

Bin Gao·Xin Liu·Xiaojun Chen·Ya-xiang Yuan
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Abstract

In this paper, we prove that the global version of the ${\L}$ojasiewicz gradient inequality holds for quadratic sphere constrained optimization problem with exponent $\theta=\frac{3}{4}$. An example from Ting Kei Pong shows that $\theta=\frac{3}{4}$ is tight. This is the first ${\L}$ojasiewicz gradient inequality established for the sphere constrained optimization problem with a linear term.

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Bin Gao, Xin Liu, Xiaojun Chen, Ya-xiang Yuan. 2016-11-27. On the {\L}ojasiewicz Exponent of the Quadratic Sphere Constrained Optimization Problem. https://arxiv.org/abs/1611.08781

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