TY - JOUR
T1 - A combined class of self-scaling and modified quasi-Newton methods
AU - Al-Baali, Mehiddin
AU - Khalfan, Humaid
PY - 2012/6
Y1 - 2012/6
N2 - 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.
AB - 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.
KW - Line-search framework
KW - Modified quasi-Newton updates
KW - Self-scaling technique
KW - Unconstrained optimization
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U2 - 10.1007/s10589-011-9415-1
DO - 10.1007/s10589-011-9415-1
M3 - Article
AN - SCOPUS:84861843748
SN - 0926-6003
VL - 52
SP - 393
EP - 408
JO - Computational Optimization and Applications
JF - Computational Optimization and Applications
IS - 2
ER -