Global Optimization for the Parameter Estimation of Differential-Algebraic Systems

2000 ◽  
Vol 39 (5) ◽  
pp. 1291-1310 ◽  
Author(s):  
William R. Esposito ◽  
Christodoulos A. Floudas
Keyword(s):  
Global Optimization ◽  
Parameter Estimation ◽  
Algebraic Systems

Parameter estimation in nonlinear algebraic models via global optimization

1998 ◽  
Vol 22 ◽  
pp. S213-S220 ◽  
Author(s):  
William R. Esposito ◽  
Christodoulos A. Floudas
Keyword(s):  
Global Optimization ◽  
Parameter Estimation ◽  
Algebraic Models

Global optimization for parameter estimation of differential-algebraic systems

2009 ◽  
Vol 63 (3) ◽  
Author(s):  
Michal Čižniar ◽  
Marián Podmajerský ◽  
Tomáš Hirmajer ◽  
Miroslav Fikar ◽  
Abderrazak Latifi
Keyword(s):  
Global Optimization ◽  
Parameter Estimation ◽  
Time Series Data ◽  
Optimization Method ◽  
Differential Algebraic Equations ◽  
Series Data ◽  
Global Optimality ◽  
Algebraic Equations ◽  
Estimation Of Parameters ◽  
Orthogonal Collocation

AbstractThe 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.

A general strategy for parameter estimation in differential—algebraic systems

1993 ◽  
Vol 17 (5-6) ◽  
pp. 517-525 ◽  
Author(s):  
P. Bilardello ◽  
X. Joulia ◽  
J.M. Le Lann ◽  
H. Delmas ◽  
B. Koehret
Keyword(s):  
Parameter Estimation ◽  
General Strategy ◽  
Algebraic Systems

Tensor based approach to the numerical treatment of the parameter estimation problems in mathematical immunology

2018 ◽  
Vol 26 (1) ◽  
pp. 51-66 ◽  
Author(s):  
Valeriya V. Zheltkova ◽  
Dmitry A. Zheltkov ◽  
Zvi Grossman ◽  
Gennady A. Bocharov ◽  
Eugene E. Tyrtyshnikov
Keyword(s):  
Global Optimization ◽  
Parameter Estimation ◽  
Optimization Techniques ◽  
Computational Method ◽  
Parameter Estimation Problem ◽  
Multiscale Models ◽  
Computational Tools ◽  
Systems Immunology ◽  
Estimation Problems ◽  
Standard Parameter

AbstractThe development of efficient computational tools for data assimilation and analysis using multi-parameter models is one of the major issues in systems immunology. The mathematical description of the immune processes across different scales calls for the development of multiscale models characterized by a high dimensionality of the state space and a large number of parameters. In this study we consider a standard parameter estimation problem for two models, formulated as ODEs systems: the model of HIV infection and BrdU-labeled cell division model. The data fitting is formulated as global optimization of variants of least squares objective function. A new computational method based on Tensor Train (TT) decomposition is applied to solve the formulated problem. The idea of proposed method is to extract the tensor structure of the optimized functional and use it for optimization. The method demonstrated a better performance in comparison with some other broadly used global optimization techniques.

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