An example of slow convergence for Newton's method on a function with globally Lipschitz continuous Hessian

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DOI	10.5286/raltr.2013004
Persistent URL	http://purl.org/net/epubs/work/65541
Record Status	Checked
Record Id	65541
Title	An example of slow convergence for Newton's method on a function with globally Lipschitz continuous Hessian
Contributors	C Cartis (Edinburgh U.), NIM Gould (STFC Rutherford Appleton Lab.), PL Toint (Namur U., Belgium)
Abstract	An example is presented where Newton's method for unconstrained minimization is applied to find an e-approximate first-order critical point of a smooth function and takes a multiple of e−2 iterations and function evaluations to terminate, which is as many as the steepest descent method in its worst-case. The novel feature of the proposed example is that the objective function has a globally Lipschitz-continuous Hessian, while a previous example published by the same authors only ensured this critical property along the path of iterates, which is impossible to verify a priori.
Organisation	STFC , SCI-COMP , SCI-COMP-CM
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Language	English (EN)

Type	Details	URI(s)	Local file(s)	Year
Report	RAL Technical Reports RAL-TR-2013-004. 2013.		RAL-TR-2013-004.pdf	2013