Convex and concave envelopes of artificial neural network activation functions for deterministic global optimization

Wilhelm, Matthew; Wang, Chenyu; Stuber, Matthew D.

doi:10.1007/s10898-022-01228-x

Cited by 4 publications

(4 citation statements)

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“…We aim to establish a robust operation problem to verify if a control recourse exists that mitigates the impacts of uncertainty. The semi-infinite constraints in this problem are Accordingly, the operation under uncertainty feasibility problem can be expressed as the following SIP: Again, the SIPres algorithm with convex/concave envelopes of activation functions was used to solve the SIP (eq ). The SIPres algorithm terminates with η* = 0.288 after a single iteration in 21.14 CPU seconds.…”

Section: Case Studiesmentioning

confidence: 99%

“…We first solved this hybrid model using the SIPres routine provided in EAGO v0.6.1 , and using the convex/concave envelope of SiLU described in a forthcoming work . The SIP was solved to an absolute tolerance of 10 –3 .…”

Section: Case Studiesmentioning

confidence: 99%

“…Again, the SIPres algorithm 12 with convex/concave envelopes of activation functions 84 was used to solve the SIP (eq 14).…”

Section: ■ Case Studiesmentioning

confidence: 99%

“…We first solved this hybrid model using the SIPres 12 routine provided in EAGO v0.6.1 63,95 and using the convex/concave envelope of SiLU described in a forthcoming work. 84 The SIP was solved to an absolute tolerance of 10 −3 . The algorithm terminated in three iterations, taking 2.9 CPU seconds when using the envelope of SiLU when computing relaxations.…”

Section: T H I S C O N T E N T Imentioning

confidence: 99%

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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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