Optimal steepest descent algorithm for experimental data fitting in nonlinear problems

In this paper, we propose the application of the steepest descent method augmented with the optimal control theory approach, in order to solve the problem of fitting phenomenological parameters in coupled nonlinear reaction-diffusion equations, which parameters do not vary in time. The penalty function and two different transformations of the inequality constraints given are considered. The necessary optimality conditions are derived using the stationary condition of the Lagrangian, and a new numerical algorithm is designed. Results for computation of the heat conduction coefficient as well as a set of parameters in a mathematical biology problem are presented.