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Belmiro P M Duarte1, Weng Kee Wong2, Nuno M C Oliveira3

  • 1Centro de Investigação em Processos Químicos e Produtos da Floresta, Department of Chemical Engineering, University of Coimbra, Pólo II, R. Sílvio Lima, 3030-790 Coimbra, Portugal. Tel. +351 239 798700; Department of Chemical and Biological Engineering, ISEC, Polytechnic Institute of Coimbra, R. Pedro Nunes, 3030-199 Coimbra, Portugal. Tel. +351 239 790200.

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|March 8, 2016
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Summary
This summary is machine-generated.

This study introduces mathematical programming for optimal model design in chemistry and chemical engineering. Semidefinite Programming (SDP) is recommended for its balance of efficiency and design quality.

Keywords:
Approximate DesignBayesian Optimal DesignGaussian Quadrature FormulaGlobal OptimizationInformation Matrix

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Area of Science:

  • Chemistry and Chemical Engineering
  • Mathematical Optimization
  • Statistical Modeling

Background:

  • Optimal experimental design is crucial for efficient model building in science and engineering.
  • Traditional methods may not efficiently handle complex models or various design criteria.

Purpose of the Study:

  • To apply mathematical programming, specifically Semidefinite Programming (SDP) and Nonlinear Programming (NLP), for optimal model design.
  • To evaluate and compare the performance of SDP and NLP formulations in generating optimal designs.
  • To investigate the impact of discretization on design generation.

Main Methods:

  • Utilized Semidefinite Programming (SDP) and Nonlinear Programming (NLP) formulations.
  • Employed local design-based setups for linear models and a Bayesian setup with Gaussian Quadrature Formulas (GQFs) for nonlinear models.
  • Applied mathematical programming to solve optimization problems after discretizing the design space.

Main Results:

  • Both SDP and NLP formulations successfully generated optimal designs (D-, A-, and E-optimal).
  • NLP produced highly efficient D-optimal designs but was computationally less efficient than SDP.
  • The efficiency of designs from both methods was comparable, with SDP being more practical.

Conclusions:

  • SDP formulation is recommended for practical applications due to its computational efficiency and comparable design quality.
  • The methodology can address challenges like heteroscedasticity in models.
  • Mathematical programming offers a robust framework for optimal experimental design.