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Abstract: In order to solve an unconstrained optimization problem, quasi-Newton methods are used when the Hessian matrix of the objective function can not be cheaply computed. In these methods, at each step, the current approximation to the Hessian matrix is updated to a new approximation satisfying the secant equation. The open question is how can we find a new approximation which maintains as much information as possible already built up in the current approximation. In this thesis we try to answer... (Update)
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.... optimal volume measure (A) trace(A) n (A) see [24] which leads to the same optimally conditioned, sized, SR1 updates, see [26]. See [26] for results on these and other condition numbers, their relations to measures for least change, and also their relations to...
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Semidefinite and Cone Programming Bibliography/Comments - Wolkowicz (2004) (Correct)
An All Inclusive Efficient Region Of Updates For Least Change .. - Wolkowicz, Zhao (1993) (Correct)
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2.0: Measures For Symmetric Rank-One Updates - Henry Wolkowicz (1990) (Correct)
1.6: Theory of Algorithms for Unconstrained Optimization - Nocedal (1992) (Correct)
1.1: Sizing and Least Change Secant Methods - Dennis, Jr., Wolkowicz (1993) (Correct)
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BibTeX entry: (Update)
Q. ZHAO. Measures for least change secant methods. PhD thesis, University of Waterloo, Waterloo, Ont, Canada, 1992. http://citeseer.ist.psu.edu/zhao92measures.html More
@mastersthesis{ zhao93measures,
author = "Qing Zhao",
title = "Measures for Least Change Secant Methods",
address = "Waterloo, ON, Canada",
year = "1993",
url = "citeseer.ist.psu.edu/zhao92measures.html" }
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