Presentation	2003/10/14 A Convergent Property of Steepest Descent Method in Minimizing Nonlinear Functions Takashi OZEKI,
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Abstract(in English)	In this paper, we discuss the limiting behavior of the search direction of the steepest descent method in minimizing general nonlinear function. It is shown that the search direction asymptotically alternates between two orthogonal directions represented by linear combinations of two eigenvectors of the Hessian matrix of nonlinear function at the minimum point in almost every case. This is similar to the phenomenon in minimizing the quadratic form. However, we also show some special case which is different from the one of the quadratic form. Moreover, we give some necessary conditions in which special cases appear.
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Keyword(in English)	Steepest Descent Method / Nonlinear Function / Iterative Method / Behavior of Convergence
Paper #	NLP2003-85
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Committee	NLP
Conference Date	2003/10/14(1days)
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Paper Information
Registration To	Nonlinear Problems (NLP)
Language	JPN
Title (in Japanese)	(See Japanese page)
Sub Title (in Japanese)	(See Japanese page)
Title (in English)	A Convergent Property of Steepest Descent Method in Minimizing Nonlinear Functions
Sub Title (in English)
Keyword(1)	Steepest Descent Method
Keyword(2)	Nonlinear Function
Keyword(3)	Iterative Method
Keyword(4)	Behavior of Convergence
1st Author's Name	Takashi OZEKI
1st Author's Affiliation	Faculty of Engineering, Fukuyama University()
Date	2003/10/14
Paper #	NLP2003-85
Volume (vol)	vol.103
Number (no)	375
Page	pp.pp.-
#Pages	6
Date of Issue