Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/8114
Title: A new class of quasi-Newton updating formulas
Authors: Li, D
Qi, L 
Roshchina, V
Keywords: Convergence
Derivative-free conditions
Positive definiteness
Rank-two quasi-Newton updating formulas
Unconstrained optimization
Issue Date: 2008
Publisher: Taylor & Francis
Source: Optimization methods and software, 2008, v. 23, no. 2, p. 237-249 How to cite?
Journal: Optimization methods and software 
Abstract: In this paper, we propose a derivative-free quasi-Newton condition, which results in a new class of quasi-Newton updating formulas for unconstrained optimization. Each updating formula in this class is a rank-two updating formula and preserves the positive definiteness of the second derivative matrix of the quadratic model. Its first two terms are the same as the first two terms of the BFGS updating formula. We establish global convergence of quasi-Newton methods based upon the updating formulas in this class, and superlinear convergence of a special quasi-Newton method among them. Then we propose a special quasi-Newton updating formula, which repetitively uses the new quasi-Newton condition. This updating formula is derivative-free. Numerical results are reported.
URI: http://hdl.handle.net/10397/8114
ISSN: 1055-6788
DOI: 10.1080/10556780701646360
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