On the Łojasiewicz Exponent of the Quadratic Sphere Constrained Optimization Problem

Abstract

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

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References in corpus (2)

• Quadratic Optimization with Orthogonality Constraints: Explicit Lojasiewicz Exponent and Linear Convergence of Line-Search Methods
• A Unified Approach to Error Bounds for Structured Convex Optimization Problems

Cited by in corpus (3)

• Global Convergence of Arbitrary-Block Gradient Methods for Generalized Polyak-Łojasiewicz Functions
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