| Presentation | 2013-10-28 Mathematical structure of optimal solutions in continuous optimization problems (2) : Necessary and sufficient optimality condition, and estimations of the number of solutions Hideo KANEMITSU, Hideyuki IMAI, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | We show mathematical structures of optimal solutions in continuous optimization problem with continuous multivariate multimodal objective function : "minimize:f(x) subject to x E S(closed bounded set)". For realizing the purpose, We show a necessary and sufficient condition that the interior point of S is optimal solution in the problem its function is Morse function. In addition, we evaluate the number of solutions in following three cases of objective function: 1) univariate polynomial functions, 2) separable functions and c) periodic unimodal functions. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | optimal solution / optimization problem / mathematical structure / multimodal function / optimization theory / nonlinear |
| Paper # | NLP2013-81 |
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| Committee | NLP |
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| Conference Date | 2013/10/21(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Registration To | Nonlinear Problems (NLP) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Mathematical structure of optimal solutions in continuous optimization problems (2) : Necessary and sufficient optimality condition, and estimations of the number of solutions |
| Sub Title (in English) | |
| Keyword(1) | optimal solution |
| Keyword(2) | optimization problem |
| Keyword(3) | mathematical structure |
| Keyword(4) | multimodal function |
| Keyword(5) | optimization theory |
| Keyword(6) | nonlinear |
| 1st Author's Name | Hideo KANEMITSU |
| 1st Author's Affiliation | Hokkaido University of Education() |
| 2nd Author's Name | Hideyuki IMAI |
| 2nd Author's Affiliation | Graduate School of Information Science and Technology Hokkaido University |
| Date | 2013-10-28 |
| Paper # | NLP2013-81 |
| Volume (vol) | vol.113 |
| Number (no) | 271 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |