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On the {\L}ojasiewicz Exponent of the Quadratic Sphere Constrained Optimization Problem
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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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Cited by 1 Pith paper
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On The Geometric Analysis of A Quartic-quadratic Optimization Problem under A Spherical Constraint
For the quartic-quadratic sphere problem, the paper characterizes all local minima in the diagonal case, proves strict-saddle properties for extreme beta, and establishes a Kurdyka-Lojasiewicz exponent of 1/4.
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