Incorporating nonmonotone strategies into the trust region method for unconstrained optimization

Authors:
Neng-zhu Gu;Jiang-tao Mo
Affiliations:
School of Business, University of Shanghai for Science and Technology, Shanghai 200093, China;College of Mathematics and Information Science, Guangxi University, Nanning 530004, China
Venue:
Computers & Mathematics with Applications
Year:
2008

Citing 11
Cited 2

A nonmonotone line search technique for Newton's method

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On a subproblem of trust region algorithms for constrained optimization

Mathematical Programming: Series A and B
A trust region algorithm for equality constrained optimization

Mathematical Programming: Series A and B
Nonmonotonic trust region algorithm

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An assessment of nonmonotone linesearch techniques for unconstrained optimization

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Testing Unconstrained Optimization Software

ACM Transactions on Mathematical Software (TOMS)
Trust-region methods

Trust-region methods
On the nonmonotone line search

Journal of Optimization Theory and Applications
Combination trust-region line-search methods for unconstrained optimization

Combination trust-region line-search methods for unconstrained optimization
A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization

SIAM Journal on Optimization
A nonmonotone trust region method based on nonincreasing technique of weighted average of the successive function values

Journal of Computational and Applied Mathematics

Combining nonmonotone conic trust region and line search techniques for unconstrained optimization

Journal of Computational and Applied Mathematics
A nonmonotone trust region method with new inexact line search for unconstrained optimization

Numerical Algorithms

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Abstract

This paper concerns a nonmonotone line search technique and its application to the trust region method for unconstrained optimization problems. In our line search technique, the current nonmonotone term is a convex combination of the previous nonmonotone term and the current objective function value, instead of an average of the successive objective function values that was introduced by Zhang and Hager [H. Zhang, W.W. Hager, A nonmonotone line search technique and its application to unconstrained optimization, SIAM J. Optim. 14 (4) (2004) 1043-1056]. We incorporate this nonmonotone scheme into the traditional trust region method such that the new algorithm possesses nonmonotonicity. Unlike the traditional trust region method, our algorithm performs a nonmonotone line search to find a new iteration point if a trial step is not accepted, instead of resolving the subproblem. Under mild conditions, we prove that the algorithm is global and superlinear convergence holds. Primary numerical results are reported.