论文标题
广义凹面kurdyka-łojasiewicz物业的确切模量
The exact modulus of the generalized concave Kurdyka-Łojasiewicz property
论文作者
论文摘要
我们通过采用非平滑降低功能，介绍了凹面kurdyka-lojasiewicz（kl）属性的广义版本。我们还介绍了广义凹入kl属性的确切模量，该模量提供了有关最佳凹入功能的开放问题的答案。确切的模量被设计为所有可能的凹面功能中最小的模量。举例说明了这一宜人的属性。反过来，使用精确的模量，我们为著名的Bolte-Sabach-Teboulle棕榈算法产生的迭代总长度提供了最清晰的上限。
We introduce a generalized version of the concave Kurdyka-Łojasiewicz (KL) property by employing nonsmooth desingularizing functions. We also present the exact modulus of the generalized concave KL property, which provides an answer to the open question regarding the optimal concave desingularizing function. The exact modulus is designed to be the smallest among all possible concave desingularizing functions. Examples are given to illustrate this pleasant property. In turn, using the exact modulus we provide the sharpest upper bound for the total length of iterates generated by the celebrated Bolte-Sabach-Teboulle PALM algorithm.
