High-Order Moreau Envelope in the Nonconvex Setting: Framework and Algorithms

Explore a 31-minute conference talk on high-order Moreau envelope in nonconvex optimization, presented by Masoud Ahookhosh at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the introduction of high-order proximal operator (HOPE) and high-order Moreau envelope (HOME) in nonconvex settings. Examine the fundamental properties of HOPE and HOME, including single-valuedness and differential properties under conditions like prox-regularity and weak-convexity. Investigate the Hölder continuity of HOPE and gradient of HOME. Learn about the development of inexact proximal point and inexact gradient methods for nonconvex optimization, including their convergence analysis and linear convergence under Kurdyka-Łojasiewicz conditions. Gain insights from preliminary numerical results that validate the theoretical foundations presented in this talk, which was part of the "One World Optimization Seminar in Vienna" workshop held at ESI in June 2024.