A Trust-Region Framework for Real-Time Optimization with Structural Process-Model Mismatch

Abstract

Advances in optimization theory, software, and modeling environments promote widespread application of optimization-based decision making. However, the gap between the optimization model and the real-world counterpart impedes optimality of the solution and leads to loss of performance in practice. To overcome this barrier, this paper proposes to reconcile the model and the real plant with iterative parameter estimation and real-time optimization based on a trust-region framework. Three algorithms are developed with different means of constructing/maintaining the local model, managing the trust-region radius, and assessing the trial point. Analysis shows that all these algorithms converge to the correct first-order KKT point despite structural model mismatch. Case studies of reduced model-based optimization demonstrate effectiveness and performance of the proposed methods.

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Acknowledgements

This paper is based on work supported by National Key Research and Development Program of China (2017YFB0603703), National Science and Technology Major Project of China (ZX06902 and ZX06906), Fundamental Research Funds for the Central Universities 2020FZZX003-01-06.

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Correspondence to Lorenz T. Biegler.

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This paper is dedicated to Professor Volker Mehrmann on his 65th birthday, with thanks especially for his advances in applied mathematics that have had strong influences on real-world problems.

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Wang, K., Yang, C., Shao, Z. et al. A Trust-Region Framework for Real-Time Optimization with Structural Process-Model Mismatch. Vietnam J. Math. 48, 809–830 (2020). https://doi.org/10.1007/s10013-020-00442-y

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Keywords

  • Trust region
  • Structural mismatch
  • Inexact model
  • Plant derivative

Mathematics Subject Classification (2010)

  • 90C30
  • 49M37
  • 90C59