THE POLYAK-LOJASIEWICZ CONDITION FOR A STRONGLY CONVEX FUNCTION ON A SMOOTH MANIFOLD AND ITS APPLICATION

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Abstract

It is shown that a strongly convex Lipschitz differentiable function satisfies the Polyak-Lojasiewicz condition on a proximally smooth C1-smooth manifold for a certain relationship of the constants of proximal smoothness of the manifold and strong convexity of the function. The mentioned condition guarantees a linear rate of convergence of the gradient projection method for minimizing a function on a manifold. An algorithm is proposed for finding the metric projection of a point located sufficiently close to a manifold onto this manifold.

About the authors

M. V Balashov

Trapeznikov Institute of Control Sciences of Russian Academy of Sciences

Email: balashov73@mail.ru
Moscow, Russia

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