Nonmonotone Alternative Direction Method Based on Simple Conic Model for Unconstrained Optimization

Lijuan Zhao ()
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Lijuan Zhao: Department of Mathematics Teaching, Nanjing Institute of Railway Technology, Nanjing 210031, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2024, vol. 41, issue 02, 1-22

Abstract: In this paper, we propose a nonmonotone Alternative Direction Method (ADM) 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 replaced by a scalar approximation, the trust region subproblem is solved by ADM which was first proposed by Zhu and Ni. When the trial point isn’t accepted by trust region, line search technique is used to find an acceptable point instead of resolving the trust region subproblem. The new method needs less memory capacitance and computational complexity. The global convergence of the algorithm is established under some mild conditions. Numerical results on a series of standard test problems are reported to show the new method is effective and robust.

Keywords: Nonmonotone; simple conic model; trust region; alternative direction method; line search (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0217595923500112

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