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...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Springer New York LLC
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/26233 |
| _version_ | 1848751927799578624 |
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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. |
| first_indexed | 2025-11-14T08:00:30Z |
| format | Journal Article |
| id | curtin-20.500.11937-26233 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:00:30Z |
| publishDate | 2015 |
| publisher | Springer New York LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |