Galerkin-Conditional-Gradient

Authors: Giacomo Cristinelli, José A. Iglesias, Daniel Walter

This module solves the control problem with Total Variation regularization

$$\underset{u\in BV(\mathrm{\Omega })}{min}\frac{1}{2}|Ku-y_o{|}^2+\alpha TV(u,\mathrm{\Omega })$$

where K is the control-to-state operator associated with a Poisson-type PDE.

It employs the method described in the paper "Conditional gradients for total variation regularization with PDE constraints: a graph cuts approach". Preprint available at: https://arxiv.org/abs/2310.19777

Important libraries:

FEniCS (Dolfin) --version 2019.1.0 (https://fenicsproject.org/)

Maxflow (http://pmneila.github.io/PyMaxflow/maxflow.html)