Optimization-based convex relaxations for nonconvex parametric systems of ordinary differential equations

Song, Yingkai; Khan, Kamil A.

doi:10.1007/s10107-021-01654-x

Cited by 10 publications

(1 citation statement)

References 71 publications

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“…Within this reduced-space context, researchers have addressed the construction of convex and concave relaxations of factorable functions ,− (i.e., a function defined by a finite recursive composition of sums, products, and univariate transcendental functions) as well as specific classes of functions that break the factorability assumption. Methods for computing relaxations of parametric solutions of differential equations ,, as well as implicit functions evaluated by fixed-point methods have both been detailed . Provided that relaxations of intermediate terms may be computed, these relaxations may be readily composed in a generalized framework .…”

Section: Optimization Of Hybrid Modelsmentioning

confidence: 99%

Semi-Infinite Optimization with Hybrid Models

Wang

Wilhelm

Stuber

2022

Ind. Eng. Chem. Res.

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The robust design of performance/safety-critical process systems, from a model-based perspective, remains an existing challenge. Hybrid first-principles data-driven models offer the potential to dramatically improve model prediction accuracy, stepping closer to the digital twin concept. Within this context, worst-case engineering design feasibility and reliability problems give rise to a class of semi-infinite program (SIP) formulations with hybrid models as coupling equality constraints. Reduced-space deterministic global optimization methods are exploited to solve this class of SIPs to ϵ-global optimality in finitely many iterations. This approach is demonstrated on two challenging case studies: a nitrification reactor for a wastewater treatment system to address worst-case feasibility verification of dynamical systems and a three-phase separation system plagued by numerical domain violations to demonstrate how they can be overcome using a nonsmooth SIP formulation with hybrid models and a validity constraint incorporated.

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