Decision theory: multicriteria techniques in multilevel optimization - Pieume, Calice Olivier
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The book addresses two important classes of optimization: multiobjective optimization and bi-level optimization. First, we develop a procedure for solving Multiple Objective Linear Programming. The method is based on a new characterization of efficient faces. It's exploits the connectedness property of the set of ideal tableaux associated to degenerate points in case of degeneracy. We also develop an approach for solving Bilevel Linear Programming Problems. It is based on the result that an optimal solution of the problem is reachable at an extreme point of the underlying region. Some…mehr

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Produktbeschreibung
The book addresses two important classes of optimization: multiobjective optimization and bi-level optimization. First, we develop a procedure for solving Multiple Objective Linear Programming. The method is based on a new characterization of efficient faces. It's exploits the connectedness property of the set of ideal tableaux associated to degenerate points in case of degeneracy. We also develop an approach for solving Bilevel Linear Programming Problems. It is based on the result that an optimal solution of the problem is reachable at an extreme point of the underlying region. Some applications of these two areas of optimization techniques are explored. An application of multicriteria optimization approach for finding an optimal planning for the distribution of electrical energy in Cameroon is provided. Similarly, a bilevel optimization model that could permit to protect any economic sector where local initiatives are threatened is proposed. Finally the relationship between the two classes of optimization is investigated. We proposed for instance new relations between the solutions of the two classes of optimization problems.
Autorenporträt
Olivier Pieume holds a PhD in Applied Mathematics (decision science) from the University of Paris Est and the University of Montreal. He is a Statistician Economist engineer and is currently working for UNESCO's International Institute for Educational Planning. Dr. Olivier Pieume has a dozen of scientific publications in international journal.