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Robust simulation and design using semi-infinite programs with implicit functions

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  • Matthew D. Stuber
  • Paul I. Barton

Abstract

A method is presented for guaranteeing robust steady-state operation of chemical processes using a model-based approach, taking into account uncertainty in the model parameters and disturbances in the process inputs. Intractable constrained max–min optimisation formulations have been proposed for this problem in the past. A new approach is presented in which the equality constraints (process model equations) are solved numerically for the process variables as implicit functions of the uncertain parameters and controls. The problem is then formulated as a semi-infinite program (SIP) constrained only by the performance specifications as semi-infinite inequality constraints. A rigorous, finite ε-optimal convergent algorithm for solving such SIPs is proposed, making no assumptions on convexity, which makes use of the novel developments of parametric interval-Newton methods for bounding implicit functions, and novel developments in McCormick relaxations of algorithms.

Suggested Citation

  • Matthew D. Stuber & Paul I. Barton, 2011. "Robust simulation and design using semi-infinite programs with implicit functions," International Journal of Reliability and Safety, Inderscience Enterprises Ltd, vol. 5(3/4), pages 378-397.
    • Handle: RePEc:ids:ijrsaf:v:5:y:2011:i:3/4:p:378-397
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    Citations

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    Cited by:

    1. Stuart M. Harwood & Paul I. Barton, 2017. "How to solve a design centering problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 215-254, August.
    2. A. Tsoukalas & A. Mitsos, 2014. "Multivariate McCormick relaxations," Journal of Global Optimization, Springer, vol. 59(2), pages 633-662, July.
    3. Alexander Mitsos & Angelos Tsoukalas, 2015. "Global optimization of generalized semi-infinite programs via restriction of the right hand side," Journal of Global Optimization, Springer, vol. 61(1), pages 1-17, January.
    4. Jason Ye & Joseph K. Scott, 2023. "Extended McCormick relaxation rules for handling empty arguments representing infeasibility," Journal of Global Optimization, Springer, vol. 87(1), pages 57-95, September.
    5. Stuber, Matthew D., 2016. "Optimal design of fossil-solar hybrid thermal desalination for saline agricultural drainage water reuse," Renewable Energy, Elsevier, vol. 89(C), pages 552-563.

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