Global optimization for parameter estimation of differential-algebraic systems
-
Michal Čižniar
,
Marián Podmajerský
Abstract
The estimation of parameters in semi-empirical models is essential in numerous areas of engineering 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 ɛ-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.
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© 2008 Institute of Chemistry, Slovak Academy of Sciences
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- A simple flow injection spectrophotometric determination method for iron(III) based on O-acetylsalicylhydroxamic acid complexation
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- Intramolecular MLOH/π and MLNH/π interactions in crystal structures of metal complexes
- A strategy for new macrocycle magnetic materials synthesis
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- New Cu(II), Co(II), and Ni(II) complexes with thieno[2,3-b]pyridine and 2-methylthieno[2,3-b]pyridine as ligands: Synthesis and crystal structures
- Synthesis of saccharide precursors for preparation of potential inhibitors of glycosyltranferases
- Simultaneous spectrophotometric determination of minoxidil and tretinoin by the H-point standard addition method and partial least squares
- Adsorption and release of terbinafine hydrochloride: Effects of adsorbents, additives, pH, and temperature
- Determination of alkaloids in Corydalis yanhusuo using hollow-fibre liquid phase microextraction and high performance liquid chromatography
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