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Gradient Projection Method on Matrix Manifolds

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The minimization of a function with a Lipschitz continuous gradient on a proximally smooth subset of a finite-dimensional Euclidean space is considered. Under the restricted secant inequality, the gradient projection… Click to show full abstract

The minimization of a function with a Lipschitz continuous gradient on a proximally smooth subset of a finite-dimensional Euclidean space is considered. Under the restricted secant inequality, the gradient projection method as applied to the problem converges linearly. In certain cases, the linear convergence of the gradient projection method is proved for the real Stiefel or Grassmann manifolds.

Keywords: method matrix; projection method; gradient projection; matrix manifolds

Journal Title: Computational Mathematics and Mathematical Physics
Year Published: 2020

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