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

B. Chachuat, M. A. Latifi
2004 Nonconvex Optimization and Its Applications  
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
more » ... e 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.
doi:10.1007/978-1-4613-0251-3_5 fatcat:vp7prp62bffbrad2zrmqvzdkta