Paper Abstract and Keywords |
Presentation |
2013-10-28 15:00
Mathematical structure of optimal solutions in continuous optimization problems (2)
-- Necessary and sufficient optimality condition, and estimations of the number of solutions -- Hideo Kanemitsu (Hokkaido Univ. of Edu.), Hideyuki Imai (Hokkaido Univ.) NLP2013-81 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
We show mathematical structures of optimal solutions in continuous optimization problem with continuous multivariate multimodal objective function : ``minimize : $f(x)$ subject to $xin S$(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) |
(in English) |
optimal solution / optimization problem / mathematical structure / multimodal function / optimization theory / nonlinear / / |
Reference Info. |
IEICE Tech. Rep., vol. 113, no. 271, NLP2013-81, pp. 63-68, Oct. 2013. |
Paper # |
NLP2013-81 |
Date of Issue |
2013-10-21 (NLP) |
ISSN |
Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 |
Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) |
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NLP2013-81 |
Conference Information |
Committee |
NLP |
Conference Date |
2013-10-28 - 2013-10-29 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Sanport Hall Takamatsu |
Topics (in Japanese) |
(See Japanese page) |
Topics (in English) |
General |
Paper Information |
Registration To |
NLP |
Conference Code |
2013-10-NLP |
Language |
Japanese |
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) |
Sub Title (in English) |
Necessary and sufficient optimality condition, and estimations of the number of solutions |
Keyword(1) |
optimal solution |
Keyword(2) |
optimization problem |
Keyword(3) |
mathematical structure |
Keyword(4) |
multimodal function |
Keyword(5) |
optimization theory |
Keyword(6) |
nonlinear |
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1st Author's Name |
Hideo Kanemitsu |
1st Author's Affiliation |
Hokkaido University of Education (Hokkaido Univ. of Edu.) |
2nd Author's Name |
Hideyuki Imai |
2nd Author's Affiliation |
Hokkaido University (Hokkaido Univ.) |
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Speaker |
Author-1 |
Date Time |
2013-10-28 15:00:00 |
Presentation Time |
15 minutes |
Registration for |
NLP |
Paper # |
NLP2013-81 |
Volume (vol) |
vol.113 |
Number (no) |
no.271 |
Page |
pp.63-68 |
#Pages |
6 |
Date of Issue |
2013-10-21 (NLP) |
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