Optimization Over the Efficient Set of Multi-objective Convex Optimal Control Problems
We consider multi-objective convex optimal control problems. First we state a relationship between the (weakly or properly) efficient set of the multi-objective problem and the solution of the problem scalarized via a convex combination of objectives through a vector of parameters (or weights). Then...
| Main Authors: | , |
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| Format: | Journal Article |
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Springer New York LLC
2010
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| Online Access: | http://hdl.handle.net/20.500.11937/23261 |
| _version_ | 1848751100877864960 |
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| author | Bonnel, Henri Kaya, C. |
| author_facet | Bonnel, Henri Kaya, C. |
| author_sort | Bonnel, Henri |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We consider multi-objective convex optimal control problems. First we state a relationship between the (weakly or properly) efficient set of the multi-objective problem and the solution of the problem scalarized via a convex combination of objectives through a vector of parameters (or weights). Then we establish that (i) the solution of the scalarized (parametric) problem for any given parameter vector is unique and (weakly or properly) efficient and (ii) for each solution in the (weakly or properly) efficient set, there exists at least one corresponding parameter vector for the scalarized problem yielding the same solution. Therefore the set of all parametric solutions (obtained by solving the scalarized problem) is equal to the efficient set. Next we consider an additional objective over the efficient set. Based on the main result, the new objective can instead be considered over the (parametric) solution set of the scalarized problem. For the purpose of constructing numerical methods, we point to existing solution differentiability results for parametric optimal control problems. We propose numerical methods and give an example application to illustrate our approach. © 2010 Springer Science+Business Media, LLC. |
| first_indexed | 2025-11-14T07:47:22Z |
| format | Journal Article |
| id | curtin-20.500.11937-23261 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:47:22Z |
| publishDate | 2010 |
| publisher | Springer New York LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-232612018-03-29T09:06:48Z Optimization Over the Efficient Set of Multi-objective Convex Optimal Control Problems Bonnel, Henri Kaya, C. We consider multi-objective convex optimal control problems. First we state a relationship between the (weakly or properly) efficient set of the multi-objective problem and the solution of the problem scalarized via a convex combination of objectives through a vector of parameters (or weights). Then we establish that (i) the solution of the scalarized (parametric) problem for any given parameter vector is unique and (weakly or properly) efficient and (ii) for each solution in the (weakly or properly) efficient set, there exists at least one corresponding parameter vector for the scalarized problem yielding the same solution. Therefore the set of all parametric solutions (obtained by solving the scalarized problem) is equal to the efficient set. Next we consider an additional objective over the efficient set. Based on the main result, the new objective can instead be considered over the (parametric) solution set of the scalarized problem. For the purpose of constructing numerical methods, we point to existing solution differentiability results for parametric optimal control problems. We propose numerical methods and give an example application to illustrate our approach. © 2010 Springer Science+Business Media, LLC. 2010 Journal Article http://hdl.handle.net/20.500.11937/23261 10.1007/s10957-010-9709-y Springer New York LLC restricted |
| spellingShingle | Bonnel, Henri Kaya, C. Optimization Over the Efficient Set of Multi-objective Convex Optimal Control Problems |
| title | Optimization Over the Efficient Set of Multi-objective Convex Optimal Control Problems |
| title_full | Optimization Over the Efficient Set of Multi-objective Convex Optimal Control Problems |
| title_fullStr | Optimization Over the Efficient Set of Multi-objective Convex Optimal Control Problems |
| title_full_unstemmed | Optimization Over the Efficient Set of Multi-objective Convex Optimal Control Problems |
| title_short | Optimization Over the Efficient Set of Multi-objective Convex Optimal Control Problems |
| title_sort | optimization over the efficient set of multi-objective convex optimal control problems |
| url | http://hdl.handle.net/20.500.11937/23261 |