Summary

Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications

2013

Session Number:A3L-C

Session:

Number:94

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

Hideo KANEMITSU,  Hideaki IMAI,  Masaaki MIYASKOSHI,  

pp.94-97

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.2.94

PDF download (304.3KB)

Summary:
We show mathematical structures on optimal solutions in a continuous optimization problem with a continuous multivariate multimodal objective function : “minimize : ƒ (x) subject to xS ⊂ 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.

References:

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