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Convex variational problems arise in many fields ranging from imageprocessing to fluid and solid mechanics communities. Interesting applicationsusually involve non-smooth terms which require well-designed optimizationalgorithms for their resolution. The present manuscript presents the Pythonpackage called fenics_optim built on top of the FEniCS finite element softwarewhich enables to automate the formulation and resolution of various convexvariational problems. Formulating such a problem relies on FEniCSdomain-specific language and the representation of convex functions, inparticular non-smooth ones, in the conic programming framework. The discreteformulation of the corresponding optimization problems hinges on the finiteelement discretization capabilities offered by FEniCS while their numericalresolution is carried out by the interior-point solver Mosek. Through variousillustrative examples, we show that convex optimization problems can beformulated using only a few lines of code, discretized in a very simple mannerand solved extremely efficiently.

Automating the formulation and resolution of convex variational problems: applications from image processing to computational mechanics