Solving convex optimization problems in function spaces (Sebastien Loisel, Heriot-Watt University)

26.03.2024 14:00 – 15:00

Many stationary partial differential equations and boundary value problems can be rephrased in terms of the minimization of a functional, sometimes called the energy, the Lagrangian, or the action. In the usual case (e.g. the usual linear Laplacian), the Lagrangian is a convex quadratic functional of its argument. We consider the generalization to nonquadratic but convex Lagrangians (e.g. the p-Laplacian, a highly nonlinear PDE operator). One may solve such problems by the barrier method on a finite element grid with $n$ vertices, but usually the performance is no better than $O(n^{1.5})$ FLOPS. We will discuss new algorithms that converge in $O^*(n)$ FLOPS, where the star indicates that certain polylogarithms are neglected.

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

entrée libre