ISSN:
1436-4646
Keywords:
Step-size Procedures
;
Line Search
;
Gradient Methods
;
Unconstrained Minimization
;
Negative Curvature
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract The Armijo and Goldstein step-size rules are modified to allow steps along a curvilinear path of the formx(α) + x + αs + α2 d, wherex is the current estimate of the minimum,s is a descent direction andd is a nonascent direction of negative curvature. By using directions of negative curvature when they exist, we are able to prove, under fairly mild assumptions, that the sequences of iterates produced by these algorithms converge to stationary points at which the Hessian matrix of the objective function is positive semidefinite.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01588294
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