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A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination.

Belmiro P M Duarte1, Weng Kee Wong2, Anthony C Atkinson3

  • 1GEPSI - PSE Group, CIEPQPF, Department of Chemical Engineering, University of Coimbra, Pólo II, R. Sílvio Lima, 3030-790 Coimbra, Portugal; Department of Chemical and Biological Engineering, ISEC, Polytechnic Institute of Coimbra, R. Pedro Nunes, 3030-199 Coimbra, Portugal.

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Summary
This summary is machine-generated.

Finding T-optimal designs for model discrimination is challenging. This study introduces a Semi-Infinite Programming (SIP) approach for a more systematic and general method to discover these optimal designs.

Keywords:
Continuous designEquivalence theoremGlobal optimizationMaximum likelihood designMinimax programSemi-Infinite Programming

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Area of Science:

  • Statistics
  • Optimization
  • Experimental Design

Background:

  • T-optimum designs are crucial for model discrimination but computationally intensive to determine.
  • Existing methods often rely on specialized numerical procedures for specific problems.
  • Analytical T-optimal designs are scarce, limiting their broader application.

Purpose of the Study:

  • To develop a more systematic and general approach for finding T-optimal designs.
  • To overcome the computational challenges associated with two-layered optimization problems.
  • To automate the construction of globally optimal designs for model discrimination.

Main Methods:

  • Reformulation of the minimax/maximin optimization problem into an equivalent Semi-Infinite Program (SIP).
  • Utilizing an exchange-based method iterating bounds from outer and inner programs to convergence.
  • Employing a global Nonlinear Programming (NLP) solver for subproblems to identify optimal designs and least favorable configurations.

Main Results:

  • The proposed SIP approach successfully generated results consistent with known T-optimal designs.
  • The method demonstrated generality across various model discrimination problems with normally distributed errors.
  • A nonlinear program was used to verify global optimality and automate design construction.

Conclusions:

  • The Semi-Infinite Programming approach offers a more systematic and general strategy for T-optimal design.
  • This method simplifies the process by requiring only numerical optimization for parameter estimation.
  • The algorithm provides a robust tool for constructing globally optimal designs in model discrimination.