The estimation of parameters in semi-empirical models is essential in numerous areas of engineer- ing and applied science. In many cases, these models are described by a set of ordinary-differential equations or by a set of differential-algebraic equations. Due to the presence of non-convexities of functions participating in these equations, current gradient-based optimization methods can guarantee only locally optimal solutions. This deficiency can have a marked impact on the operation of chemical processes from the economical, environmental and safety points of view and it thus motivates the development of global optimization algorithms. This paper presents a global optimization method which guarantees ε-convergence to the global solution. The approach consists in the transformation of the dynamic optimization problem into a nonlinear programming problem (NLP) using the method of orthogonal collocation on finite elements. Rigorous convex underestimators of the nonconvex NLP problem are employed within the spatial branch-and-bound method and solved to global optimality. The proposed method was applied to two example problems dealing with parameter estimation from time series data.
| author | = | {M. {\v{C}}i\v{z}niar and M. Podmajersk\'y and T. Hirmajer and M. Fikar and M. A. Latifi}, |
| title | = | {Global optimization for parameter estimation of differential-algebraic systems}, |
| journal | = | {Chemical Papers}, |
| year | = | {2009}, |
| keyword | = | {identifik\'acia parametrov, ortogon\'alna kolok\'acia, dynamick\'a optimaliz\'acia, glob\'alna optimaliz\'acia}, |
| volume | = | {63}, |
| number | = | {3}, |
| pages | = | {274-283}, |
| annote | = | {The estimation of parameters in semi-empirical models is essential in numerous areas of engineer- ing and applied science. In many cases, these models are described by a set of ordinary-differential equations or by a set of differential-algebraic equations. Due to the presence of non-convexities of functions participating in these equations, current gradient-based optimization methods can guarantee only locally optimal solutions. This deficiency can have a marked impact on the operation of chemical processes from the economical, environmental and safety points of view and it thus motivates the development of global optimization algorithms. This paper presents a global optimization method which guarantees ε-convergence to the global solution. The approach consists in the transformation of the dynamic optimization problem into a nonlinear programming problem (NLP) using the method of orthogonal collocation on finite elements. Rigorous convex underestimators of the nonconvex NLP problem are employed within the spatial branch-and-bound method and solved to global optimality. The proposed method was applied to two example problems dealing with parameter estimation from time series data. }, |
| url | = | {https://www.uiam.sk/assets/publication_info.php?id_pub=788} |