Variational optimisation by the solution of a series of Hamilton–Jacobi equations

We present a unified scheme which, by combining backward differentiation formulae and variational optimisation theory, significantly extends the scope of both concepts and their application to optimisation problems wherein the constituent dynamics consist of widely disparate scales. Our approach is based on the time-integration of a series of matrix Riccati expressions which satisfy a Hamilton–Jacobi equation. © 2001 Elsevier Science B.V. All rights reserved.