Title: Newtonian Methods in Nonsmooth Optimization via the Lens of Variational Analysis

Abstract: This talk presents the results of the local and global convergence of our Newton-type methods for solving structured nonconvex and nonsmooth optimization problems, utilizing tools from variational analysis and generalized differentiation. The methods employ generalized Hessians (coderivatives of subgradient mappings) associated with objective functions. These objective functions are either prox-bounded functions or represented as the sum of a smooth function and an extended-real-valued (not necessarily smooth) function. Additionally, we introduce a new line search method, a generalization of the proximal gradient method, to globalize our coderivative-based Newton methods by incorporating the machinery of forward-backward envelopes. Further applications to l0-l2 least square regression problems are also introduced.

Thanh Phat Vo
Assistant Professor of Mathematics
Department of Mathematics & Statistics
University of North Dakota
101 Cornell St. Stop 8376
324 Witmer Hall
Grand Forks, ND 58202, USA
Google Site: https://sites.google.com/view/vtphat204