How bad are the BFGS and DFP methods when the objective function is quadratic?
Mathematical Programming: Series A and B
A tool for the analysis of Quasi-Newton methods with application to unconstrained minimization
SIAM Journal on Numerical Analysis
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
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We propose a modified BFGS method and study the global and superlinear convergence properties of this method. We show that under certain circumstances this modified BFGS method has a better mechanism of correcting the eigenvalues. This modified method can also be regarded as an implementation technique of the standard BFGS method.