Skip to main
Math equations
George Mason University
Events

Applied & Computational Mathematics seminar: Proximal Galerkin: A Unified Framework for Variational Problems with Inequality Constraints

Aug 29, 2025, 10:00 - 11:00 AM

 

Speaker:  Brendan Keith, Brown University


Title:  Proximal Galerkin: A Unified Framework for Variational Problems with Inequality Constraints

 

Abstract:  This talk presents the Proximal Galerkin (PG) method, a high-order numerical method for solving variational problems with inequality constraints. PG combines two foundational ideas from applied mathematics: Galerkin discretizations of partial differential equations and Bregman proximal point algorithms for nonsmooth or constrained optimization. Each iteration of the method solves a regularized subproblem formulated as a nonlinear saddle-point system. Conceptually, PG is a discretized gradient flow within a finite-dimensional function space, such as a finite element subspace, yielding robust and convergent solution approximations. The unified framework systematically handles a broad class of variational inequalities, enabling high-order, constraint-preserving solutions without the need for specialized basis functions. This talk will outline the theoretical foundations of PG, highlight its connections to convex analysis, and showcase recent applications in contact mechanics, fracture, and multi-phase flows, among others. 

 

Time:  Friday, August 29 – 10:00am

Place:  Exploratory Hall, room 4106 and Zoom

* The programs and services offered by George Mason University are open to all who seek them. George Mason does not discriminate on the basis of race, color, religion, ethnic national origin (including shared ancestry and/or ethnic characteristics), sex, disability, military status (including veteran status), sexual orientation, gender identity, gender expression, age, marital status, pregnancy status, genetic information, or any other characteristic protected by law. After an initial review of its policies and practices, the university affirms its commitment to meet all federal mandates as articulated in federal law, as well as recent executive orders and federal agency directives.