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

Authors:
Zhaocheng Cui;Boying Wu;Shaojian Qu
Affiliations:
Department of Mathematics, Faculty of Science, Harbin Institute of Technology, Harbin 150080, China;Department of Mathematics, Faculty of Science, Harbin Institute of Technology, Harbin 150080, China;Natural Science Research Center, Harbin Institute of Technology, Harbin 150080, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

In this paper, we propose a trust region method for unconstrained optimization that can be regarded as a combination of conic model, nonmonotone and line search techniques. Unlike in traditional trust region methods, the subproblem of our algorithm is the conic minimization subproblem; moreover, our algorithm performs a nonmonotone line search to find the next iteration point when a trial step is not accepted, instead of resolving the subproblem. The global and superlinear convergence results for the algorithm are established under reasonable assumptions. Numerical results show that the new method is efficient for unconstrained optimization problems.