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Using sparse-grid methods to improve computation efficiency in solving dynamic nonlinear chance-constrained optimization problems / Michael Kloppel in Industrial & engineering chemistry research, Vol. 50 N° 9 (Mai 2011) 

Public ISBD [article]  in Industrial & engineering chemistry research > Vol. 50 N° 9 (Mai 2011) . - pp. 5693–5704 Titre : Using sparse-grid methods to improve computation efficiency in solving dynamic nonlinear chance-constrained optimization problems Type de document : texte imprimé Auteurs : Michael Kloppel, Auteur ; Abebe Geletu, Auteur ; Armin Hoffmann, Auteur Année de publication : 2011 Article en page(s) : pp. 5693–5704 Note générale : Chimie industrielle Langues : Anglais (eng) Mots-clés : Optimization Résumé : Chance-constrained programming is known as a suitable approach to optimization under uncertainty. However, a serious difficulty is the requirement of evaluating the probability of holding inequality constraints through the numerical computation of multidimensional integrals. If a nonlinear system with many uncertain variables is considered, the computational load will be prohibitive when using a full-grid integration method. Thus our aim is to investigate a method to decrease the computation expense in solving nonlinear chance-constrained optimization problems with many uncertain variables. In particular, we consider dynamic nonlinear process optimization under uncertainty, which will be transferred into a nonlinear chance-constrained optimization problem by a discretization scheme. To solve this problem, we propose to use sparse-grid methods for the evaluation of the objective function, the probability of constraint satisfaction, and their gradients. These components are implemented in a nonlinear programming framework. A dynamic mixing process is taken to illustrate its computation efficiency. It can be shown that the computation time will be significantly reduced using the sparse-grid method, in comparison to using full-grid methods. DEWEY : 660 ISSN : 0888-5885 En ligne : http://pubs.acs.org/doi/abs/10.1021/ie102426w [article] Using sparse-grid methods to improve computation efficiency in solving dynamic nonlinear chance-constrained optimization problems [texte imprimé] / Michael Kloppel, Auteur ; Abebe Geletu, Auteur ; Armin Hoffmann, Auteur . - 2011 . - pp. 5693–5704. Chimie industrielle Langues : Anglais (eng) in Industrial & engineering chemistry research > Vol. 50 N° 9 (Mai 2011) . - pp. 5693–5704 Mots-clés : Optimization Résumé : Chance-constrained programming is known as a suitable approach to optimization under uncertainty. However, a serious difficulty is the requirement of evaluating the probability of holding inequality constraints through the numerical computation of multidimensional integrals. If a nonlinear system with many uncertain variables is considered, the computational load will be prohibitive when using a full-grid integration method. Thus our aim is to investigate a method to decrease the computation expense in solving nonlinear chance-constrained optimization problems with many uncertain variables. In particular, we consider dynamic nonlinear process optimization under uncertainty, which will be transferred into a nonlinear chance-constrained optimization problem by a discretization scheme. To solve this problem, we propose to use sparse-grid methods for the evaluation of the objective function, the probability of constraint satisfaction, and their gradients. These components are implemented in a nonlinear programming framework. A dynamic mixing process is taken to illustrate its computation efficiency. It can be shown that the computation time will be significantly reduced using the sparse-grid method, in comparison to using full-grid methods. DEWEY : 660 ISSN : 0888-5885 En ligne : http://pubs.acs.org/doi/abs/10.1021/ie102426w