We consider the minimization problem for a nonconvex function with Lipschitz continuous gradient on a proximally smooth (possibly nonconvex) subset of a finite-dimensional Euclidean space. We introduce the error bound condition with exponent ##IMG## [http://ej.iop.org/images/1064-5616/211/4/481/MSB_211_4_481ieqn1.gif] {$\alpha\in (0,1]$} for the gradient mapping. Under this condition, it is shown that the standard gradient projection algorithm converges to a solution of the problem linearly or sublinearly, depending on the value of the exponent ##IMG## [http://ej.iop.org/images/1064-5616/211/4/481/MSB_211_4_481ieqn2.gif] {$\alpha$} . This paper is theoretical. Bibliography: 23 titles.

中文翻译：

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Lipschitz连续梯度函数和近端平滑集的梯度投影算法

我们考虑有限维欧氏空间近端平滑（可能是非凸）子集上具有Lipschitz连续梯度的非凸函数的最小化问题。我们以指数## IMG ## [http://ej.iop.org/images/1064-5616/211/4/481/MSB_211_4_481ieqn1.gif] {$ \ alpha \ in（0,1 ] $}用于梯度映射。在这种情况下，表明标准梯度投影算法可以线性或亚线性地收敛到问题的解，具体取决于指数## IMG ## [http：// ej .iop.org / images / 1064-5616 / 211/4/481 / MSB_211_4_481ieqn2.gif] {$ \ alpha $}。本文是理论性的，参考书目：23种。