ISSN:
1436-4646
Keywords:
Unconstrained Optimization
;
Modified Newton's Method
;
Descent Pairs
;
Directions of Negative Curvature
;
Symmetric Indefinite Factorization
;
Steplength Algorithm
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract We present a modified Newton method for the unconstrained minimization problem. The modification occurs in non-convex regions where the information contained in the negative eigenvalues of the Hessian is taken into account by performing a line search along a path which is initially tangent to a direction of negative curvature. We give termination criteria for the line search and prove that the resulting iterates are guaranteed to converge, under reasonable conditions, to a critical point at which the Hessian is positive semidefinite. We also show how the Bunch and Parlett decomposition of a symmetric indefinite matrix can be used to give entirely adequate directions of negative curvature.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01582091
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