Journal Article

FZJ-2020-02628

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Analysis of the local well‐posedness of optimization‐constrained differential equations by local optimality conditions

Zhao, X. ; Ploch, T. ; Noack, S.FZJ* ; Wiechert, W.FZJ* ; Mitsos, A. (Corresponding author)FZJ* ; von Lieres, E. (Corresponding author)FZJ*

2020
Wiley Hoboken, NJ

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Please use a persistent id in citations: http://hdl.handle.net/2128/26190  doi:10.1002/aic.16548

Abstract: Optimization‐constrained differential equations (OCDE) are a class of mathematical problems where differential equations are constrained by an embedded algebraic optimization problem. We analyze the well‐posedness of the local solutions of OCDE based on local optimality. By assuming linear independence constraint qualification and applying the Karush‐Kuhn‐Tucker optimality conditions, an OCDE is transformed into a complementarity system (CS). Under second‐order sufficient condition we show that (a) if strict complementary condition (SCC) holds, the local solution of OCDE is well‐posed, which corresponds to a mode of the derived CS; (b) at points where SCC is violated, a local solution of OCDE exists by sequentially connecting the local solutions of two selected modes of the derived CS. We propose an event‐based algorithm to numerically solve OCDE. We illustrate the approach and algorithm for microbial cultivation, single flash unit and contrived numerical examples.

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Contributing Institute(s):

1. Biotechnologie (IBG-1)
2. Modellierung von Energiesystemen (IEK-10)

Research Program(s):

1. 583 - Innovative Synergisms (POF3-583) (POF3-583)

Appears in the scientific report 2020

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Engineering, Computing and Technology ; DEAL Wiley ; Essential Science Indicators ; IF < 5 ; JCR ; Nationallizenz ; SCOPUS ; Science Citation Index ; Science Citation Index Expanded ; Web of Science Core Collection

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