A numerical method for variational problems over the cone of convex functions

Details A numerical method for variational problems over the cone of convex functions A numerical method for variational problems over the cone of convex functions

2011-07-26

arxiv.org/abs/1107.5290v2

Mathematics

Numerical Analysis

21 pages, 6 figures, 6 tables

Scientific paper

We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. The problem is at the interface between convex analysis, convex optimization, variational problems and Partial Differential Equation (PDE) techniques. The approach is to approximate the (non-polyhedral) cone of convex functions by a polyhedral cone which can be represented by linear inequalities. This approach leads theoretical quantitative estimates of the approximate convexity of solutions and an optimization problem with linear constraints which can be computed efficiently.

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