Abstract
This paper presents a new nonmonotone filter line search technique in association with the MBFGS method for solving unconstrained minimization. The filter method, which is traditionally used for constrained nonlinear programming (NLP), is extended to solve unconstrained NLP by converting the latter to an equality constrained minimization. The nonmonotone idea is employed to the filter method so that the restoration phrase, a common feature of most filter methods, is not needed. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. The results of numerical experiments indicate that the proposed method is efficient.
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This research is supported by the National Science Foundation under Grant No. 11371253 and the Science Foundation under Grant No. 11C0336 of Provincial Education Department of Hunan.
This paper was recommended for publication by Editor ZHANG Hanqin.
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Wang, Z., Zhu, D. A nonmonotone filter line search technique for the MBFGS method in unconstrained optimization. J Syst Sci Complex 27, 565–580 (2014). https://doi.org/10.1007/s11424-014-1081-9
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DOI: https://doi.org/10.1007/s11424-014-1081-9