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The Gradient Projection Algorithm for Smooth Sets and Functions in Nonconvex Case

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We consider the problem of minimization for a function with Lipschitz continuous gradient on a proximally smooth and smooth manifold in a finite dimensional Euclidean space. We consider the Lezanski-Polyak-Lojasiewicz… Click to show full abstract

We consider the problem of minimization for a function with Lipschitz continuous gradient on a proximally smooth and smooth manifold in a finite dimensional Euclidean space. We consider the Lezanski-Polyak-Lojasiewicz (LPL) conditions in this problem of constrained optimization. We prove that the gradient projection algorithm for the problem converges with a linear rate when the LPL condition holds.

Keywords: algorithm smooth; projection algorithm; gradient projection; smooth sets; sets functions

Journal Title: Set-valued and Variational Analysis
Year Published: 2020

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