INTERVAL ANALYSIS FOR GUARANTEED NONLINEAR PARAMETER ESTIMATION

摘要

Interval analysis was initially developed to analyze and control numerical errors in computers. It can now be used to solve problems that are at the core of nonlinear parameter estimation, such as the minimization of possibly nonconvex cost functions or the characterization of sets defined by nonlinear inequalities. The solutions obtained are approximate but guaranteed, in the sense that no solution can be lost, a definite advantage over the usual local iterative techniques. After recalling basic concepts of interval analysis, this introductory paper describes algorithmic tools that can be used for nonlinear parameter estimation and applies them to simple illustrative examples drawn from compartmental modeling, a formalism widely used in biology. Guaranteed numerical integrators and properties of cooperative systems make it possible to deal with differential models, even when they do not admit closed-form solutions. Pointers to freely downloadable software are provided.