On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization

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DOI	10.5286/raltr.2012007
Persistent URL	http://purl.org/net/epubs/work/62442
Record Status	Checked
Record Id	62442
Title	On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization
Contributors	C Cartis (Edinburgh U.), NIM Gould (STFC Rutherford Appleton Lab.), PL Toint (Facultes Universitaires ND de la Paix, Belgium)
Abstract	We propose a new termination criteria suitable for potentially singular, zero or non-zero residual, least-squares problems, with which cubic regularization variants take at most O(epsilon−3/2) residual- and Jacobian-evaluations to drive either the residual or a scaled gradient of the least-squares function below epsilon; this is the best-known bound for potentially singular nonlinear least-squares problems. We then apply the new optimality measure and cubic regularization steps to a family of least-squares merit functions in the context of a target-following algorithm for nonlinear equality-constrained problems; this approach yields the first evaluation complexity bound of order epsilon−3/2 for nonconvexly constrained problems when higher accuracy is required for primal feasibility than for dual first-order criticality.
Organisation	CSE , CSE-NAG , STFC
Keywords
Funding Information
Related Research Object(s):	10940855
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Language	English (EN)

Type	Details	URI(s)	Local file(s)	Year
Report	RAL Technical Reports RAL-TR-2012-007. 2012.		RAL-TR-2012-007 (2).pdf	2012