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

Proceedings

Conference Short	NOLTA
Conference Name	Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications
Conference Year	2013
Session Number	A3L-C
Session Name	[RS] Control and Optimization
Number	94
Session Date	2013/09/09

Title	Definitions and Properties of (Local) Minima and Multimodal Functions using Level Set for Continuous Optimization Problems
Author	Hideo KANEMITSU, Hideaki IMAI, Masaaki MIYASKOSHI,
Vo.No. start page.end page	Vol.2, No.94, pp.94-97
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Abstract	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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