2020/08/30 by Xianfu Wang, Ziyuan Wang, Wang, Xianfu +1
Engineering · Mathematics · #Control Systems and Identification #Approximation Theory and Sequence Spaces #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2008.13257
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.