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 computationa l standpoint. The method involves the minimization of a weighted sum o f 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 me thods tailored for this formulation, although computationally efficien t, can only attain convergence to a local solution. In this paper, a g lobal 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 nonl inear algebraic models. The proposed convexification techniques exploi t the mathematical properties of the formulation. Classical nonlinear estimation problems were solved and will be used to illustrate the var ious theoretical and computational aspects of the proposed approach.