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

Understand

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.