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An Active Set Modified Polak–Ribiére–Polyak Method for Large-Scale Nonlinear Bound Constrained Optimization

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Abstract

In this paper, we propose an active set modified Polak–Ribiére–Polyak method for solving large-scale optimization with simple bounds on the variables. The active set is guessed by an identification technique at each iteration and the recently developed modified Polak–Ribiére–Polyak method is used to update the variables with indices outside of the active set. Under appropriate conditions, we show that the proposed method is globally convergent. Numerical experiments are presented using box constrained problems in the CUTEr test problem libraries.

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Acknowledgements

We would like to thank the referees for their detailed comments and suggestions that have led to a significant improvement of the paper. We also thank the Professors E.G. Birgin, J.M. Martínez, and M. Raydan for their SPG2 code and Professors W.W.Hager and H. Zhang for their ASA code for numerical comparison. W. Cheng’s research was supported by the NSF of China via grant (11071087, 11101081) and by Foundation for Distinguished Young Talents in Higher Education of Guangdong, China LYM10127. D. Li’s research is supported by the major project of the Ministry of Education of China Grant 309023 and the NSF of China Grant 11071087.

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Authors and Affiliations

  1. College of Computer, Dongguan University of Technology, Dongguan, 523808, China

    Wanyou Cheng

  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. Donghui Li
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Correspondence to Wanyou Cheng.

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Communicated by F. Giannessi.

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Cheng, W., Li, D. An Active Set Modified Polak–Ribiére–Polyak Method for Large-Scale Nonlinear Bound Constrained Optimization. J Optim Theory Appl 155, 1084–1094 (2012). https://doi.org/10.1007/s10957-012-0091-9

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  • DOI: https://doi.org/10.1007/s10957-012-0091-9

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