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DOI 10.5286/raltr.2015011
Persistent URL http://purl.org/net/epubs/work/23648311
Record Status Checked
Record Id 23648311
Title Improved worst-case evaluation complexity for potentially rank-deficient nonlinear least-Euclidean-norm problems using higher-order regularized models
Abstract Given a sufficiently smooth vector-valued function r(x), a local minimizer of kr(x)k2 within a closed, non-empty, convex set F is sought by modelling kr(x)kq 2/q with a p-th order Taylor-series approximation plus a (p + 1)-st order regularization term for given even p and some appropriate associated q. The resulting algorithm is guaranteed to find a value ¯x for which kr(¯x)k2 ? ?p or ?(¯x) ? ?d, for some first-order criticality measure ?(x) of kr(x)k2 within F, using at most O(max{max(?d, ?min)?(p+1)/p,max(?p, rmin)?1/2i }) evaluations of r(x) and its derivatives; here rmin and ?min ? 0 are any lower bounds on kr(x)k2 and ?(x), respectively, and 2i is the highest power of 2 that divides p. An improved bound is possible under a suitable full-rank assumption.
Organisation STFC , SCI-COMP , SCI-COMP-CM
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Licence Information: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Technical Reports RAL-TR-2015-011. 2015. RAL-TR-2015-011.pdf 2015