Definitions and Properties of (Local) Minima and Multimodal Functions using Level Set for Continuous Optimization Problems

国際会議講演論文

会議略称	NOLTA
国際会議名称	Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications
開催年	2013
セッション番号	A3L-C
セッション名	[RS] Control and Optimization
講演番号	94
開催日(セッション)	2013/09/09

タイトル	Definitions and Properties of (Local) Minima and Multimodal Functions using Level Set for Continuous Optimization Problems
著者名	Hideo KANEMITSU, Hideaki IMAI, Masaaki MIYASKOSHI,
Vo.No. 開始ページ.終了ページ	Vol.2, No.94, pp.94-97
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要旨	We show mathematical structures on optimal solutions in a continuous optimization problem with a continuous multivariate multimodal objective function : “minimize : ƒ (x) subject to x ∈ S ⊂ ℜⁿ. For realizing the purpose, we show definitions of (local) minima using neighborhood of each minimum and using some types of level set. Moreover, we describe relationship among the previous definitions and new definitions of (local) minima, differences of concept of solutions, and the number of solutions especially in case where there exists flat regions on a function. The new definitions in this paper is simpler than the previous definitions of (local) minima.
DOI	10.15248/proc.2.94
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