How bad are the BFGS and DFP methods when the objective function is quadratic?
Mathematical Programming: Series A and B
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Variational quasi-Newton methods for unconstrained optimization
Journal of Optimization Theory and Applications
Computational Optimization and Applications
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Variable metric methods for unconstrainted optimization and nonlinear least squares
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
A modified BFGS method and its global convergence in nonconvex minimization
Journal of Computational and Applied Mathematics - Special issue on nonlinear programming and variational inequalities
Limited-Memory Reduced-Hessian Methods for Large-Scale Unconstrained Optimization
SIAM Journal on Optimization
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited
ACM Transactions on Mathematical Software (TOMS)
The Superlinear Convergence of a Modified BFGS-Type Method for Unconstrained Optimization
Computational Optimization and Applications
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Local and superlinear convergence of quasi-Newton methods based on modified secant conditions
Journal of Computational and Applied Mathematics
A new class of quasi-Newton updating formulas
Optimization Methods & Software - Dedicated to Professor Michael J.D. Powell on the occasion of his 70th birthday
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Techniques for obtaining safely positive definite Hessian approximations with self-scaling and modified quasi-Newton updates are combined to obtain `better' curvature approximations in line search methods for unconstrained optimization. It is shown that this class of methods, like the BFGS method, has the global and superlinear convergence for convex functions. Numerical experiments with this class, using the well-known quasi-Newton BFGS, DFP and a modified SR1 updates, are presented to illustrate some advantages of the new techniques. These experiments show that the performance of several combined methods are substantially better than that of the standard BFGS method. Similar improvements are also obtained if the simple sufficient function reduction condition on the steplength is used instead of the strong Wolfe conditions.