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An accurate active set conjugate gradient algorithm with project search for bound constrained optimization

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Abstract

In the paper, we propose an active set identification technique which accurately identifies active constraints in a neighborhood of an isolated stationary point without strict complementarity conditions. Based on the identification technique, we propose a conjugate gradient algorithm for large-scale bound constrained optimization. In the algorithm, the recently developed modified Polak-Ribiére-Polyak method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. Under appropriate conditions, we show that the proposed method is globally convergent. Numerical experiments are presented using bound constrained problems in the CUTEr test problem library.

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Acknowledgments

Supported by the NSF of China via grant 11071087, 11101081 and by Foundation for Distinguished Young Talents in Higher Education of Guangdong, China LYM10127 and the NSF of Dongguan University of Technology via grant ZN100024.

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Authors and Affiliations

  1. College of Computer, Dongguan University of Technology, Dongguan,  523000, China

    Wanyou Cheng & Qunfeng Liu

  2. School of Mathematical Sciences, South China Normal University, Guangzhou,  510631, China

    Donghui Li

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  1. Wanyou Cheng
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  2. Qunfeng Liu
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  3. Donghui Li
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Correspondence to Wanyou Cheng.

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Cheng, W., Liu, Q. & Li, D. An accurate active set conjugate gradient algorithm with project search for bound constrained optimization. Optim Lett 8, 763–776 (2014). https://doi.org/10.1007/s11590-013-0609-6

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  • DOI: https://doi.org/10.1007/s11590-013-0609-6

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