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Global optimization for parameter estimation of differential-algebraic systems
Čižniar, Michal, Podmajerský, Marián, Hirmajer, Tomáš, Fikar, Miroslav and Latifi, Abderrazak M. Global optimization for parameter estimation of differential-algebraic systems Chemical Papers, Vol.63, No. 3, 2009, 274-283
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Document type:
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Článok z časopisu / Journal Article |
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Collection:
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Chemical papers
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| Author(s) |
Čižniar, Michal
Podmajerský, Marián
Hirmajer, Tomáš
Fikar, Miroslav
Latifi, Abderrazak M.
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| Title |
Global optimization for parameter estimation of differential-algebraic systems
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| Journal name |
Chemical Papers
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| Publication date |
2009
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| Year available |
2009
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| Volume number |
63
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| Issue number |
3
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| ISSN |
0366-6352
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| Start page |
274
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| End page |
283
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| Place of publication |
Poland
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| Publisher |
Versita
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| Collection year |
2009
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| Language |
english
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| Subject |
290000 Engineering and Technology
290600 Chemical Engineering
290602 Process Control and Simulation
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| Abstract/Summary |
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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