Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness

Panagiotis Patrinos, Konstantinos Oikonomidis, Jan Quan, Emanuel Laude

Keywords: nonconvex optimization, generalized smoothness, first-order methods

Abstract: We analyze nonlinearly preconditioned gradient methods for solving smooth minimiza- tion problems. We introduce a generalized smoothness property, based on the notion of abstract convexity, that is broader than Lipschitz smoothness and provide sufficient first- and second-order conditions. Notably, our framework encapsulates algorithms associated with the clipping gradient method and brings out novel insights for the class of (L0,L1)- smooth functions that has received widespread interest recently, thus allowing us to go beyond already established methods. We investigate the convergence of the proposed method in both the convex and nonconvex setting.

Submission Number: 139