Semivectorial Bilevel Optimization on Riemannian Manifolds

Henri Bonnel (), Léonard Todjihoundé () and Constantin Udrişte ()
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Henri Bonnel: Université de la Nouvelle-Calédonie
Léonard Todjihoundé: Institut de Mathématiques et de Sciences Physiques
Constantin Udrişte: University Politehnica of Bucharest

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 2, No 3, 464-486

Abstract: Abstract In this paper, we deal with the semivectorial bilevel problem in the Riemannian setting. The upper level is a scalar optimization problem to be solved by the leader, and the lower level is a multiobjective optimization problem to be solved by several followers acting in a cooperative way inside the greatest coalition and choosing among Pareto solutions with respect to a given ordering cone. For the so-called optimistic problem, when the followers choice among their best responses is the most favorable for the leader, we give optimality conditions. Also for the so-called pessimistic problem, when there is no cooperation between the leader and the followers, and the followers choice may be the worst for the leader, we present an existence result.

Keywords: Multiobjective optimization on Riemannian manifolds; Semivectorial bilevel optimization problem; Bilevel optimization; 49K30; 49K35; 49K99; 58E17; 91A12; 91A65; 90C29 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-015-0789-6

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