Nonmonotone curvilinear line search methods for unconstrained optimization

Nonmonotone curvilinear line search methods for unconstrained optimization

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Article ID: iaor19981343
Country: Netherlands
Volume: 6
Issue: 2
Start Page Number: 117
End Page Number: 136
Publication Date: Sep 1996
Journal: Computational Optimization and Applications
Authors: , ,
Abstract:

We present a new algorithmic framework for solving unconstrained minimization problems that incorporates a curvilinear linesearch. The search direction used in our framework is a combination of an approximate Newton direction and a direction of negative curvature. Global convergence to a stationary point where the Hessian matrix is positive semidefinite is exhibited for this class of algorithms by means of a nonmonotone stabilization strategy. An implementation using the Bunch–Parlett decomposition is shown to outperform several other techniques on a large class of test problems.

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