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.

中文翻译：

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矩阵流形上的梯度投影方法

摘要

考虑在有限维欧氏空间的近侧光滑子集上具有Lipschitz连续梯度的函数的最小化。在受限割线不等式下，应用于该问题的梯度投影方法线性收敛。在某些情况下，对于实际的Stiefel或Grassmann流形，证明了梯度投影方法的线性收敛。