Paper Info
Title
A nonmonotone truncated Newton-Krylov method exploiting negative curvature directions, for large scale unconstrained optimization
Abstract
We propose a new truncated Newton method for large scale unconstrained optimization, where a Conjugate Gradient (CG)-based technique is adopted to solve Newton’s equation. In the current iteration, the Krylov method computes a pair of search directions: the first approximates the Newton step of the quadratic convex model, while the second is a suitable negative curvature direction. A test based on the quadratic model of the objective function is used to select the most promising between the two search directions. Both the latter selection rule and the CG stopping criterion for approximately solving Newton’s equation, strongly rely on conjugacy conditions. An appropriate linesearch technique is adopted for each search direction: a nonmonotone stabilization is used with the approximate Newton step, while an Armijo type linesearch is used for the negative curvature direction. The proposed algorithm is both globally and superlinearly convergent to stationary points satisfying second order necessary conditions. We carry out a significant numerical experience in order to test our proposal.
Year
DOI
Venue
2009
10.1007/s11590-009-0132-y
Optimization Letters
Keywords
Field
DocType
truncatednewtonmethods ·conjugatedirections ·negativecurvatures · nonmonotone stabilization technique · second order necessary conditions,satisfiability,objective function,second order,conjugate gradient
Conjugate gradient method,Newton–Krylov method,Mathematical optimization,Mathematical analysis,Quadratic equation,Conjugacy class,Regular polygon,Newton's method in optimization,Stationary point,Negative curvature,Mathematics
Journal
Volume
Issue
ISSN
3
4
1862-4480
Citations 
PageRank 
References 
4
0.48
11
Authors
2
Name
Order
Citations
PageRank
Giovanni Fasano110010.54
Stefano Lucidi278578.11