Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization

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DOI	10.5286/raltr.2010030
Persistent URL	http://purl.org/net/epubs/work/54091
Record Status	Checked
Record Id	54091
Title	Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization
Contributors	C Cartis (Edinburgh U.), NIM Gould (STFC Rutherford Appleton Lab.), PL Toint (Facultes Universaires ND de la Paix)
Abstract	algorithms described in Cartis, Gould & Toint (2009, 2010) for unconstrained (nonconvex) optimization are shown to have improved worst-case efficiency in terms of the function-and gradient-evaluation count when applied to convex and strongly convex objectives. In particular, our complexity upper bounds match in order (as a function of the accuracy of approximation), and sometimes even improve, those obtained by Nesterov (2004, 2008) and Nesterov & Polyak (2006) for these same problem classes, without employing the Hessian?s Lipschitz constant explicitly in the algorithms or requiring exact or global solution of the subproblem. An additional outcome of our approximate approach is that our complexity results can naturally capture the advantages of both first- and second-order methods.
Organisation	CSE , CSE-NAG , STFC
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Language	English (EN)

Type	Details	URI(s)	Local file(s)	Year
Report	RAL Technical Reports RAL-TR-2010-030. 2010.		RAL-TR-2010-030.pdf	2010