Higher order optimality conditions and numerical validation of local optimality ***position filled***

• Location: Imperial College - London 
• Secondment: Inria Saclay - Ile de France

• Application deadline: Position filled
• Contact: Richard Vinter

Standard second order sufficient conditions of optimality imply not only that a putative minimizer is a true, local minimizer, but that the minimizer is locally unique. They do not cover optimal control problems then, in which minimizers are not unique. There are many important cases in which uniqueness is not present (when perhaps the cost is invariant under rotations, time translations, etc.). We aim to derive second order sufficient conditions covering some of these cases. We also intend to develop numerical schemes, related to this work, for assessing when a control, obtained by applying an algorithm based on first order necessary conditions, is in fact locally optimal.