Updating the regularization parameter in the adaptive cubic regularization algorithm

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DOI	10.5286/raltr.2011007
Persistent URL	http://purl.org/net/epubs/work/55309
Record Status	Checked
Record Id	55309
Title	Updating the regularization parameter in the adaptive cubic regularization algorithm
Contributors	NIM Gould (STFC Rutherford Appleton Lab.), M Porcelli (Facultes Universaires ND de la Paix, Belgium), PL Toint (Facultes Universaires ND de la Paix, Belgium)
Abstract	The adaptive cubic regularization method (Cartis, Gould & Toint, Math. Programming, DOI: 10.1007/s10107-009-0286-5& 10.1007/s10107-009-0337-y) has been recently proposed for solving unconstrained minimization problems. At each iteration of this method, the objective function is replaced by a cubic approximation which comprises an adaptive regu-larization parameter whose role is related to the local Lipschitz constant of the objective's Hessian. We present new updating strategies for this parameter based on interpolation techniques, which improve the overall numerical performance of the algorithm. Numerical experiments on large nonlinear least-squares problems are provided.
Organisation	CSE , CSE-NAG , STFC
Keywords	cubic regularization , numerical performance , AMS classification : 49J52, 49M37, 65F22, 65K05, 90C26, 90C30, 90c55 , unconstrained optimization
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Language	English (EN)

Type	Details	URI(s)	Local file(s)	Year
Report	RAL Technical Reports RAL-TR-2011-007. 2011.		RAL-TR-2011-007.pdf	2011