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Paper Abstract and Keywords
Presentation 2014-01-21 10:00
Mathematical structures of optimal solutions in continuous optimization problems (3) -- Estimation of the number of isolated local minima and the number of connected components of local minimal values sets --
Hideo Kanemitsu (Hokkaido Univ. of Education) NLP2013-129
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 : $f(bx)$ subject to $xin S$(closed bounded set). For this purpose, first, to examine the existence condition of the minimum point of the case of general functions and multivariate polynomial functions in unconstrained optimization problem.
In addition, we have two evaluations as follows: 1) a evaluation of number of solution in case where all solutions are isolated local minima(i.e. finite number of local minima), 2) a evaluation of the number of connected components for all set of local minimal values set.
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. 383, NLP2013-129, pp. 1-6, Jan. 2014.
Paper # NLP2013-129 
Date of Issue 2014-01-14 (NLP) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
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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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Conference Information
Committee NLP  
Conference Date 2014-01-21 - 2014-01-22 
Place (in Japanese) (See Japanese page) 
Place (in English) Niseko Park Hotel 
Topics (in Japanese) (See Japanese page) 
Topics (in English) General 
Paper Information
Registration To NLP 
Conference Code 2014-01-NLP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Mathematical structures of optimal solutions in continuous optimization problems (3) 
Sub Title (in English) Estimation of the number of isolated local minima and the number of connected components of local minimal values sets 
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 Education)
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Speaker Author-1 
Date Time 2014-01-21 10:00:00 
Presentation Time 20 minutes 
Registration for NLP 
Paper # NLP2013-129 
Volume (vol) vol.113 
Number (no) no.383 
Page pp.1-6 
#Pages
Date of Issue 2014-01-14 (NLP) 


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