The open archive for STFC research publications

You may experience service outages on ePubs over the coming days due to work being carried out to enhance our network infrastructure. The service should be considered at risk from 23/11 - 03/12.

Full Record Details

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
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
Funding Information
Related Research Object(s): 10940855
Licence Information:
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