Semivectorial Bilevel Optimization on Riemannian Manifolds

© 2015, Springer Science+Business Media New York. 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...

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Main Authors: Bonnel, Henri, Todjihoundé, L., Udriste, C.
Format: Journal Article
Published: Springer New York LLC 2015
Online Access:http://hdl.handle.net/20.500.11937/26233
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author Bonnel, Henri
Todjihoundé, L.
Udriste, C.
author_facet Bonnel, Henri
Todjihoundé, L.
Udriste, C.
author_sort Bonnel, Henri
building Curtin Institutional Repository
collection Online Access
description © 2015, Springer Science+Business Media New York. 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.
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publishDate 2015
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spelling curtin-20.500.11937-262332017-09-13T15:26:00Z Semivectorial Bilevel Optimization on Riemannian Manifolds Bonnel, Henri Todjihoundé, L. Udriste, C. © 2015, Springer Science+Business Media New York. 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. 2015 Journal Article http://hdl.handle.net/20.500.11937/26233 10.1007/s10957-015-0789-6 Springer New York LLC restricted
spellingShingle Bonnel, Henri
Todjihoundé, L.
Udriste, C.
Semivectorial Bilevel Optimization on Riemannian Manifolds
title Semivectorial Bilevel Optimization on Riemannian Manifolds
title_full Semivectorial Bilevel Optimization on Riemannian Manifolds
title_fullStr Semivectorial Bilevel Optimization on Riemannian Manifolds
title_full_unstemmed Semivectorial Bilevel Optimization on Riemannian Manifolds
title_short Semivectorial Bilevel Optimization on Riemannian Manifolds
title_sort semivectorial bilevel optimization on riemannian manifolds
url http://hdl.handle.net/20.500.11937/26233