Section: New Results

Formal proofs for convex optimization problems

Participants : Benjamin Werner [Contact] , Victor Magron.

Victor Magron is working on the integration of tools that can deal with inequalities on semi-symbolic expressions with real numbers inside proof assistants like Coq .

In particular, he is working on new means to provide formally established bounds for multivariate inequalities, using methods inspired from the convex optimization literature like sums of squares (SOS) and the related semi-definite programming (SDP) relaxation.

He has implemented in OCaml a new algorithm which detects and computes automatically the possible bounds of a given expression. He has tested the approach using benchmarks largely built from inequalities issued from the formal proof of Kepler conjecture (by Thomas Hales). The algorithm computes approximation of transcendental functions by solving sum of squares problems, delegated to an external, dedicated tool. The next step of this project is to certify the correctness of these computations using the Coq system.

He has also improved a Coq tactic based on the external computation of decompositions into sums of squares originally developed by Fréderic Besson (INRIA Rennes - Bretagne Atlantique). The improvement consists in linking this tactic with a tool developed by David Monniaux (Verimag).