On the Łojasiewicz exponent of the quadratic sphere constrained optimization problem

Abstract

In this paper, we prove that the global version of the Łojasiewicz 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 Łojasiewicz gradient inequality established for the sphere constrained optimization problem with a linear term.