Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
A tool for the analysis of Quasi-Newton methods with application to unconstrained minimization
SIAM Journal on Numerical Analysis
Convergence of quasi-Newton matrices generated by the symmetric rank one update
Mathematical Programming: Series A and B
Sizing and least-change secant methods
SIAM Journal on Numerical Analysis
Sizing the BFGS and DFP updates: numerical study
Journal of Optimization Theory and Applications
Computational experience with known variable metric updates
Journal of Optimization Theory and Applications
An Adaptive Nonlinear Least-Squares Algorithm
ACM Transactions on Mathematical Software (TOMS)
Global Analysis of the Dennis--Wolkowicz Least-Change Secant Algorithm
SIAM Journal on Optimization
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
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In this paper, we analyze the global convergence of the least-change secant method proposed by Dennis and Wolkowicz, when applied to convex objective functions. One of the most distinguished features of this method is that the Dennis-Wolkowicz update doesn't necessarily belong to the Broyden convex family and can be close to the DFP update, but it still has the self-correcting property. We prove that, for convex objective functions, this method with the commonly used Wolfe line search is globally convergent. We also provide some numerical results.