On the nonmonotone line search
Journal of Optimization Theory and Applications
Quartic Formulation of Standard Quadratic Optimization Problems
Journal of Global Optimization
Mathematics of Operations Research
Iterative computation of negative curvature directions in large scale optimization
Computational Optimization and Applications
Nonmonotone projected gradient methods based on barrier and Euclidean distances
Computational Optimization and Applications
Global convergence of the nonmonotone MBFGS method for nonconvex unconstrained minimization
Journal of Computational and Applied Mathematics
Computational Optimization and Applications
SIAM Journal on Optimization
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The aim of this paper is to define a new class of minimization algorithms for solving large scale unconstrained problems. In particular we describe a stabilization framework, based on a curvilinear linesearch, which uses a combination of a Newton-type direction and a negative curvature direction. The motivation for using negative curvature direction is that of taking into account local nonconvexity of the objective function. On the basis of this framework, we propose an algorithm which uses the Lanczos method for determining at each iteration both a Newton-type direction and an effective negative curvature direction. The results of extensive numerical testing are reported together with a comparison with the LANCELOT package. These results show that the algorithm is very competitive, which seems to indicate that the proposed approach is promising.