A New Approach in Deterministic Global Optimisation of Problems with Ordinary Differential Equations

This paper presents an alternative approach to the deterministic global optimisation of problems with ordinary differential equations in the constraints. The algorithm uses a spatial branch-and-bound approach and a novel procedure to build convex underestimation of nonconvex problems is developed. Each nonconvex functional in the original problem is underestimated by adding a separate convex quadratic term. Two approaches are presented to compute rigorous values for the weight coefficients of the quadratic terms used to relax implicitly known state-dependent functionals. The advantages of the proposed underestimation procedure are that no new decision variables nor constraints are introduced in the relaxed problem, and that functionals with state-dependent integral terms can be directly handled. The resulting global optimisation algorithm is illustrated on several case studies which consist in parameter estimation and simple optimal control problems.