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DOI 10.5286/raltr.2013004
Persistent URL http://purl.org/net/epubs/work/65541
Record Status Checked
Record Id 65541
Title An example of slow convergence for Newton's method on a function with globally Lipschitz continuous Hessian
Abstract An example is presented where Newton's method for unconstrained minimization is applied to find an e-approximate first-order critical point of a smooth function and takes a multiple of e−2 iterations and function evaluations to terminate, which is as many as the steepest descent method in its worst-case. The novel feature of the proposed example is that the objective function has a globally Lipschitz-continuous Hessian, while a previous example published by the same authors only ensured this critical property along the path of iterates, which is impossible to verify a priori.
Organisation STFC , SCI-COMP , SCI-COMP-CM
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Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Technical Reports RAL-TR-2013-004. 2013. RAL-TR-2013-004.pdf 2013