TY  - JOUR
AU  - Zhao, Xiao
AU  - Ploch, Tobias
AU  - Noack, Stephan
AU  - Wiechert, Wolfgang
AU  - Mitsos, Alexander
AU  - von Lieres, Eric
TI  - Analysis of the local well‐posedness of optimization‐constrained differential equations by local optimality conditions
JO  - AIChE journal
VL  - 66
IS  - 10
SN  - 1547-5905
CY  - Hoboken, NJ
PB  - Wiley
M1  - FZJ-2020-02628
SP  - e16548
PY  - 2020
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000564202600001
DO  - DOI:10.1002/aic.16548
UR  - https://juser.fz-juelich.de/record/878094
ER  -