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Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

Postal Subscription Code 80-964

2018 Impact Factor: 0.565

Front. Math. China    2008, Vol. 3 Issue (1) : 133-148    https://doi.org/10.1007/s11464-008-0001-5
Adaptive nonmonotone line search method for unconstrained optimization
ZHOU Qunyan1, SUN Wenyu2
1.School of Mathematics and Computer Science, Nanjing Normal University;Department of Basic Science, Jiangsu Teacher University of Technology; 2.School of Mathematics and Computer Science, Nanjing Normal University;
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Abstract In this paper, an adaptive nonmonotone line search method for unconstrained minimization problems is proposed. At every iteration, the new algorithm selects only one of the two directions: a Newton-type direction and a negative curvature direction, to perform the line search. The nonmonotone technique is included in the backtracking line search when the Newton-type direction is the search direction. Furthermore, if the negative curvature direction is the search direction, we increase the steplength under certain conditions. The global convergence to a stationary point with second-order optimality conditions is established. Some numerical results which show the efficiency of the new algorithm are reported.
Issue Date: 05 March 2008
 Cite this article:   
ZHOU Qunyan,SUN Wenyu. Adaptive nonmonotone line search method for unconstrained optimization[J]. Front. Math. China, 2008, 3(1): 133-148.
 URL:  
https://academic.hep.com.cn/fmc/EN/10.1007/s11464-008-0001-5
https://academic.hep.com.cn/fmc/EN/Y2008/V3/I1/133
1 Bunch J R Parlett B N Direct methods for solvingsymmetric indefinite systems of linear equationsSIAM J Nume Anal 1971 8639655.
doi:10.1137/0708060
2 Deng N Y Xiao Y Zhou F Y A nonmonotonic trust region algorithmJournal of Optimization Theory and Applications 1993 76259285.
doi:10.1007/BF00939608
3 Ferris M C Lucidi S Roma M Nonmonotone curvilinear line search methods for unconstrainedoptimizationComputational Optimizationand Applications 1996 6117136
4 Fu J Sun W Nonmonotone adaptive trust-regionmethod for unconstrained optimization problemsApplied Mathematics and Computation 2005 163489504.
doi:10.1016/j.amc.2004.02.011
5 Grippo L Lamparillo F Lucidi S A nonmonotone line search technique for New-ton's methodSIAM J Numer Anal 1986 23707716.
doi:10.1137/0723046
6 Gould N I M Lucidi S Roma M et al.Exploiting negative curvature directions in linesearchmethods for unconstrained optimizationOptimizationMethods and Software 2000 147598.
doi:10.1080/10556780008805794
7 Lucidi S Rochetich F Roma M Curvilinear stabilization techniques for truncate Newtonmethods in large scale unconstrained optimizationSIAM J Optimization 1998 3916939.
doi:10.1137/S1052623495295250
8 Lampariello F Sciandrone M Use of the minimum-norm searchdirection in a non-monotone version of the Gauss-Newton methodJournal of Optimization Theory and Applications 2003 1196582.
doi:10.1023/B:JOTA.0000005041.99777.af
9 McCormick G P Amodification of Armijo's step-size rule for negative curvatureMathematical Programming 1977 13111115.
doi:10.1007/BF01584328
10 Moré J J Garbow B S Hillstrom K E Testing unconstrained optimization softwareACM Trans Math Software 1981 71741.
doi:10.1145/355934.355936
11 Moré J J Sorensen D C On the use of directions ofnegative curvature in a modified Newton methodMathematical Programming 1979 16120.
doi:10.1007/BF01582091
12 Nocedal J Wright S J Numerical OptimizationNew YorkSpringer 1999
13 Sun W Nonmonotoneoptimization methods: motivation and developmentIn: International Conference on Numerical Linear Algebra and Optimization,Guilin, China October 7–10, 2003 (Invited talk)
14 Sun W Nonmonotonetrust-region method for solving optimization problemsApplied Mathematics and Computation 2004 156159174.
doi:10.1016/j.amc.2003.07.008
15 Sun W Han J Sun J On global convergence of nonmonotone decent methodJ Comput Appl Math 2002 1468998.
doi:10.1016/S0377‐0427(02)00420‐X
16 Yuan Y Sun W Optimization Theory and MethodsBeijingSciencePress 1997
17 Zhou H Sun W Nonmonotone descent algorithmfor nonsmooth unconstrained optimization problemsInternational Journal of Pure and Applied Mathematics 2003 9153163
18 Zhou Q Sun W A nonmonotone second ordersteplength method for unconstrained optimizationJournal of Computational Mathematics 2007 23104112
19 Zhang J Xu C A class of indefinite doglegpath methods for unconstrained minimizationSIAM J Optimization 1999 3646667.
doi:10.1137/S105262349627523X
20 Zhang J L Zhang X S A nonmonotone adaptive trustregion method and its convergenceComputersand Mathematics with Applications 2003 4514691477.
doi:10.1016/S0898‐1221(03)00130‐5
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