If a function $f$ satisfies the Polyak-Lojasiewicz (PL) condition, that is, $$\Vert \nabla f \Vert^2 \ge 2\mu(f(x)-f^*),$$ is the function strongly convex in a certain neighborhood of the optimal solution $x^*$? Or equivalently, for a stationary point of $f$ (PL condition implies that all stationary points are global optimum), is there a neighborhood such that the function is strongly convex?
2026-04-13 19:54:37.1776110077
Can Polyak-Lojasiewicz (PL) condition imply local strong convexity?
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Every constant function satisfies (PL).