Global optimization in parameter estimation of nonlinear algebraic models via the error-in-variables approach

The estimation of parameters in nonlinear algebraic models through the error-in-variables method has been widely studied from a computational standpoint. The method involves the minimization of a weighted sum of squared errors subject to the model equations. Due to the nonlinear nature of the models used, the resulting formulation is nonconvex and may contain several local minima in the region of interest. Current methods tailored for this formulation, although computationally efficient, can only attain convergence to a local solution. In this paper, a global optimization approach based on a branch and bound framework and convexification techniques for general twice differentiable nonlinear optimization problems is proposed for the parameter estimation of nonlinear algebraic models. The proposed convexification techniques exploit the mathematical properties of the formulation. Classical nonlinear estimation problems were solved and will be used to illustrate the various theoretical and computational aspects of the proposed approach.