Abstract
The geometric modeling of mixture manufacturing management in petrochemical engineering led to consider some particular polytopes called zonotopes. The management criterion used implied the resolution of a constraint nonlinear optimization problem. Data`s problem are constituted of some measured specifications of basic product and hence subject to errors. We study the variation of the optimization problem solution with respect to data. We characterize the confident region of the solution when errors are assumed to be Gaussian and independent. Zonoids are the limit, in Hausdorff metric sense, of a sequence of zonotopes. The geometric modeling of continue manufacturing processes led to consider some particular zonoids called zonoids associated to parametric curves. We give some properties of such convex sets, we present a parametrization of the their boundaries surfaces and we study under some hypothesis the regularity of this parametrization knowing the regularity of the parametric curve. Finally, we tackle the problem of approximation of zonoids by zonotopes in Hausdorff metric sense. A constructive method of zonotope sequences which converge to a given zonoids have been established. For each zonotope, element of such sequences, we evaluate the approximation error. The convergence rates of this sequences is given. (author). 69 refs., 77 figs., 24
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Citation Formats
Daoudi, O.
Zonotopes and zonoids: studies and applications to separation processes.
France: N. p.,
1995.
Web.
Daoudi, O.
Zonotopes and zonoids: studies and applications to separation processes.
France.
Daoudi, O.
1995.
"Zonotopes and zonoids: studies and applications to separation processes."
France.
@misc{etde_251447,
title = {Zonotopes and zonoids: studies and applications to separation processes}
author = {Daoudi, O}
abstractNote = {The geometric modeling of mixture manufacturing management in petrochemical engineering led to consider some particular polytopes called zonotopes. The management criterion used implied the resolution of a constraint nonlinear optimization problem. Data`s problem are constituted of some measured specifications of basic product and hence subject to errors. We study the variation of the optimization problem solution with respect to data. We characterize the confident region of the solution when errors are assumed to be Gaussian and independent. Zonoids are the limit, in Hausdorff metric sense, of a sequence of zonotopes. The geometric modeling of continue manufacturing processes led to consider some particular zonoids called zonoids associated to parametric curves. We give some properties of such convex sets, we present a parametrization of the their boundaries surfaces and we study under some hypothesis the regularity of this parametrization knowing the regularity of the parametric curve. Finally, we tackle the problem of approximation of zonoids by zonotopes in Hausdorff metric sense. A constructive method of zonotope sequences which converge to a given zonoids have been established. For each zonotope, element of such sequences, we evaluate the approximation error. The convergence rates of this sequences is given. (author). 69 refs., 77 figs., 24 tabs.}
place = {France}
year = {1995}
month = {Oct}
}
title = {Zonotopes and zonoids: studies and applications to separation processes}
author = {Daoudi, O}
abstractNote = {The geometric modeling of mixture manufacturing management in petrochemical engineering led to consider some particular polytopes called zonotopes. The management criterion used implied the resolution of a constraint nonlinear optimization problem. Data`s problem are constituted of some measured specifications of basic product and hence subject to errors. We study the variation of the optimization problem solution with respect to data. We characterize the confident region of the solution when errors are assumed to be Gaussian and independent. Zonoids are the limit, in Hausdorff metric sense, of a sequence of zonotopes. The geometric modeling of continue manufacturing processes led to consider some particular zonoids called zonoids associated to parametric curves. We give some properties of such convex sets, we present a parametrization of the their boundaries surfaces and we study under some hypothesis the regularity of this parametrization knowing the regularity of the parametric curve. Finally, we tackle the problem of approximation of zonoids by zonotopes in Hausdorff metric sense. A constructive method of zonotope sequences which converge to a given zonoids have been established. For each zonotope, element of such sequences, we evaluate the approximation error. The convergence rates of this sequences is given. (author). 69 refs., 77 figs., 24 tabs.}
place = {France}
year = {1995}
month = {Oct}
}