%A Michael C. Ferris
%A Stefano Lucidi
%A Massimo Roma
%T Nonmonotone Curvilinear Stabilization Techniques for Unconstrained Optimization
%D October 1994
%R 94-16
%I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN
%C MADISON, WI
%X 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.