Semi-Newton Method in Difference Programming

Explore a groundbreaking approach to nonsmooth optimization problems in this 28-minute conference talk delivered by Boris Mordukhovich at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into a novel Newton-type algorithm designed for solving problems where the objective is represented as a difference of two generally nonconvex functions. Discover how this method utilizes advanced tools of variational analysis and the coderivative generated second-order subdifferential. Examine the well-posedness properties of the algorithm under general requirements and learn about its constructive convergence rates established using additional assumptions, including the Kurdyka--Lojasiewicz condition. Investigate applications of this algorithm to a general class of nonsmooth nonconvex problems in structured optimization, encompassing optimization problems with explicit constraints. Gain insights into practical applications in biochemical models and constrained quadratic programming, and compare the advantages of this new approach to existing techniques through numerical experiments. This talk, part of the "One World Optimization Seminar in Vienna" workshop, is based on joint work with F. J. Aragon-Artacho (University of Alicante) and P. Perez-Aros (University of Chile).