A trust-region method applied to parameter identification of a simple prey–predator model

Abstract

In this paper, the calibration of the non linear Lotka–Volterra model is used to compare the robustness and efficiency (CPU time) of different optimisation algorithms. Five versions of a quasi-Newton trust-region algorithm are developed and compared with a widely used quasi-Newton method. The trust-region algorithms is more robust and three of them are numerically cheaper than the more usual line search approach. Computation of the first derivatives of the objective function is cheaper with the backward differentiation (or adjoint model) technique than with the forward method as soon as the number of parameter is greater than a few ones. In the optimisation problem, the additional information about the Jacobian matrix made available by the forward method reduces the number of iterations but does not compensate for the increased numerical costs. A quasi-Newton trust-region algorithm with backward differentiation and BFGS update after both successful and unsuccessful iterations represents a robust and efficient algorithm that can be used to calibrate very demanding dynamic models.