2020/08/30 by Xianfu Wang, Ziyuan Wang, Wang, Xianfu +1 · 1 citation
Engineering · Mathematics · #Approximation Theory and Sequence Spaces #Control Systems and Identification #Mathematical Analysis and Transform Methods #math.OC #msc:26A51 #msc:26B25 #msc:26D10 #msc:49J52 #msc:90C26
paper · pdf · doi:10.48550/arxiv.2008.13257
To appear on Mathematics of Operations Research. Fixed a display error in the previous version
arxiv created 2021/10/13 · arxiv updated 2021/10/15
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.