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Contributions à l'optimisation multicritère

Abstract : The aim of this work is to study multiobjective optimization problems with or without dynamics and the generalized Bolza problem and its applications. After having pointed out some concepts of nonsmooth analysis, we begin the first part of this thesis with the existence of Lagrange multipliers for multiobjective optimization problems in infinite dimension with a general preference. We introduce the regularity of preference and use calmness qualification condition we establish the existence of Karush-Kuhn-Tucker multipliers. This allows us to obtain Fritz-John multipliers in terms of the approximate subdifferential by Ioffe. Then we derive similar results when the preference is defined by a convex cone or by an utility function. The second part deals with generalized Bolza problem. We establish necessary optimality conditions in terms of limiting Fréchet subdifferential without convexity assumptions. This result enables us to obtain the results by Vinter-Zheng and Ioffe-Rockafellar and to establish maximum principle including a new Euler-Lagrange inclusion. We apply this last one to isoperimetric problems, to the general Ramsey model of economic growth and to a chemical engineering problem. Using the notion of preference of the first part and the results of the second part we establish in the third part necessary optimality conditions and Hamiltonian conditions to multiobjective dynamic optimization. We give similar results in the case of a preference defined by a convex cone or an utility function.
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https://tel.archives-ouvertes.fr/tel-00004337
Contributor : Said Bellaassali <>
Submitted on : Friday, January 30, 2004 - 12:51:50 PM
Last modification on : Saturday, April 20, 2019 - 1:23:46 AM
Long-term archiving on: : Wednesday, November 23, 2016 - 3:53:40 PM

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  • HAL Id : tel-00004337, version 2

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Said Bellaassali. Contributions à l'optimisation multicritère. Mathématiques [math]. Université de Bourgogne, 2003. Français. ⟨tel-00004337v2⟩

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