A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
A truncated Newton method with nonmonotone line search for unconstrained optimization
Journal of Optimization Theory and Applications
Avoiding the Maratos effect by means of a nonmonotone line search I. general constrained problems
SIAM Journal on Numerical Analysis
An assessment of nonmonotone linesearch techniques for unconstrained optimization
SIAM Journal on Scientific Computing
Trust-region methods
SIAM Journal on Optimization
Regularized Newton Methods for Convex Minimization Problems with Singular Solutions
Computational Optimization and Applications
A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization
SIAM Journal on Optimization
Cubic regularization of Newton method and its global performance
Mathematical Programming: Series A and B
Affine conjugate adaptive Newton methods for nonlinear elastomechanics
Optimization Methods & Software
Regularized Newton method for unconstrained convex optimization
Mathematical Programming: Series A and B - Series B - Special Issue: Nonsmooth Optimization and Applications
Mathematical Programming: Series A and B
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In this paper we present a new class of algorithms for computing points that satisfy second order necessary optimality conditions for unconstrained minimization problems. We introduce a framework based on a curvilinear line search using a combination of a direction of negative curvature and a Newton-type descent direction which covers the scheme proposed by Moré and Sorensen [Math. Program., 16 (1979), pp. 1-20]. We then propose two kinds of descent direction from which two new algorithms emerge. One is a Levenberg-Marquardt direction, while the other is a cubic regularized Newton direction. Global convergence results and asymptotic quadratic rate are proven under mild assumptions.