Past Event: Oden Institute Seminar

The Latent Variable Proximal Point Method: A New Solver Paradigm for Variational Inequalities, Nonlinear PDEs, and Beyond

Thomas Surowiec, Chief Research Scientist, Simula Research Laboratory, Oslo, Norway

Abstract

The Latent Variable Proximal Point (LVPP) method is a novel, geometry‐encoding scheme in which the continuous level informs the algorithms, discretization techniques, and implementation. Mathematically speaking, it embeds the problem at hand into a sequence of related saddle‐point problems by introducing a structure‐preserving transformation between a latent Banach space and the feasible set. LVPP arises at the confluence of information geometry, optimization, and convex analysis through its use of proximal point methods, Legendre functions, and the isomorphisms induced by their gradients. The method yields algorithms with mesh‐independent convergence behaviour for obstacle problems, contact, topology optimization, fracture, plasticity, and more; in many cases, for the first time. 

Biography

Thomas M. Surowiec is Chief Research Scientist and Head of the Department of Numerical Analysis and Scientific Computing at Simula Research Laboratory in Oslo, Norway, where he also serves as Deputy Representative to the Board of Directors. Prior to joining Simula in late 2022, he was Professor of Mathematics at Philipps-Universität Marburg, leading the Working Group on Optimization from 2016 to 2022. From 2014 to 2016, he served as Assistant Professor in the Department of Mathematics at Humboldt-Universität zu Berlin, where he also earned his PhD in 2010 and worked as a postdoctoral researcher until 2014. Dr. Surowiec’s research spans variational analysis, optimization under uncertainty, and novel approaches to nonsmooth PDE-constrained optimization. Most recently, he has been interested in using these ideas to develop new, structure-preserving methods for the numerical solution of variational inequalities and nonlinear partial differential equations.