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000878094 1001_ $$0P:(DE-Juel1)165698$$aZhao, Xiao$$b0
000878094 245__ $$aAnalysis of the local well‐posedness of optimization‐constrained differential equations by local optimality conditions
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000878094 520__ $$aOptimization‐constrained differential equations (OCDE) are a class of mathematical problems where differential equations are constrained by an embedded algebraic optimization problem. We analyze the well‐posedness of the local solutions of OCDE based on local optimality. By assuming linear independence constraint qualification and applying the Karush‐Kuhn‐Tucker optimality conditions, an OCDE is transformed into a complementarity system (CS). Under second‐order sufficient condition we show that (a) if strict complementary condition (SCC) holds, the local solution of OCDE is well‐posed, which corresponds to a mode of the derived CS; (b) at points where SCC is violated, a local solution of OCDE exists by sequentially connecting the local solutions of two selected modes of the derived CS. We propose an event‐based algorithm to numerically solve OCDE. We illustrate the approach and algorithm for microbial cultivation, single flash unit and contrived numerical examples.
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000878094 7001_ $$0P:(DE-HGF)0$$aPloch, Tobias$$b1
000878094 7001_ $$0P:(DE-Juel1)129050$$aNoack, Stephan$$b2
000878094 7001_ $$0P:(DE-Juel1)129076$$aWiechert, Wolfgang$$b3
000878094 7001_ $$0P:(DE-Juel1)172025$$aMitsos, Alexander$$b4$$eCorresponding author
000878094 7001_ $$0P:(DE-Juel1)129081$$avon Lieres, Eric$$b5$$eCorresponding author
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