A Nonmonotone Adaptive Trust Region Method Based on Simple Conic Model for Unconstrained Optimization

ZHAO Lijuan; SUN Wen-Yu

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A Nonmonotone Adaptive Trust Region Method Based on Simple Conic Model for Unconstrained Optimization

ZHAO Lijuan 1,SUN Wen-Yu 2

1.Department of social science teaching, Nanjing Institute of Railway Technology, Nanjing, 210031

2.School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210023

*Correspondence author

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Funding: theSpecialized Research Fund of Doctoral Program of Higher Education ofChina （No.grant No. 20103207110002）, the Fund for Innovative Program of Jiangsu Province（No.grant No. CXLX12_0387）

Opened online: 5 November 2013

Accepted by: none

Citation: ZHAO Lijuan,SUN Wen-Yu.A Nonmonotone Adaptive Trust Region Method Based on Simple Conic Model for Unconstrained Optimization[OL]. [ 5 November 2013] http://en.paper.edu.cn/en_releasepaper/content/4566783

In this paper, we propose a nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional trust region method, the subproblem in our method is a simple conic model, where the Hessian of the objective function is approximated by a scalar matrix. The trust region radius is adjusted with a new self-adaptive adjustment strategy which makes use of the information of the previous iteration and current iteration. The new method needs less memory and computational complexity. The global convergence and $Q$-superlinear convergence of the algorithm are established under the mild conditions. Numerical results on a series of standard test problems are reported to show that the new method is effective and attractive for large scale unconstrained optimization problems.

Keywords:nonmonotone technique, conic model, trust region method, large scale optimization, global convergence.

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