Speaker
Patrick Farrell, University of Oxford
Abstract
The latent variable proximal point (LVPP) algorithm is a new framework for solving infinite-dimensional variational problems with inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretisation.
LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides. In many cases this mesh independence is achieved for the first time. The framework also extends to more complex constraints, gracefully handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution.
In this talk we describe the LVPP algorithm in a general form and apply it to a number of problems from across mathematics.