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Simple examples for the failure of Newton's method with line search for strictly convex minimization.
- Source :
-
Mathematical Programming . Jul2016, Vol. 158 Issue 1/2, p23-34. 12p. - Publication Year :
- 2016
-
Abstract
- In this paper two simple examples of a twice continuously differentiable strictly convex function $$f$$ are presented for which Newton's method with line search converges to a point where the gradient of $$f$$ is not zero. The first example uses a line search based on the Wolfe conditions. For the second example, some strictly convex function $$f$$ is defined as well as a sequence of descent directions for which exact line searches do not converge to the minimizer of $$f$$ . Then $$f$$ is perturbed such that these search directions coincide with the Newton directions for the perturbed function while leaving the exact line search invariant. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00255610
- Volume :
- 158
- Issue :
- 1/2
- Database :
- Academic Search Index
- Journal :
- Mathematical Programming
- Publication Type :
- Academic Journal
- Accession number :
- 116123071
- Full Text :
- https://doi.org/10.1007/s10107-015-0913-2