On the {\L}ojasiewicz Exponent of the Quadratic Sphere Constrained   Optimization Problem
  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. 
Bin Gao, Xin Liu, Xiaojun Chen and Ya-xiang Yuan
math.OC