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A smoothing projected Newton-type algorithm for semi-infinite programming

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Abstract

This paper presents a smoothing projected Newton-type method for solving the semi-infinite programming (SIP) problem. We first reformulate the KKT system of the SIP problem into a system of constrained nonsmooth equations. Then we solve this system by a smoothing projected Newton-type algorithm. At each iteration only a system of linear equations needs to be solved. The feasibility is ensured via the aggregated constraint under some conditions. Global and local superlinear convergence of this method is established under some standard assumptions. Preliminary numerical results are reported.

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Authors and Affiliations

  1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon Tong, Kowloon, Hong Kong

    Liqun Qi

  2. School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, 310018, China

    Chen Ling

  3. Institute of Mathematics, Changsha University of Science and Technology, Changsha, China

    Xiaojiao Tong

  4. Department of Mathematics and Statistics, Curtin University of Technology, Bentley, Western Australia, Australia

    Guanglu Zhou

Authors
  1. Liqun Qi
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  2. Chen Ling
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  3. Xiaojiao Tong
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  4. Guanglu Zhou
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Corresponding author

Correspondence to Liqun Qi.

Additional information

Qi’s work is supported by the Hong Kong Research Grant Council.

Ling’s work was supported by the Zhejiang Provincial National Science Foundation of China (Y606168).

Tong’s work was done during her visit to The Hong Kong Polytechnic University. Her work is supported by the NSF of China (60474070) and the Technology Grant of Hunan (06FJ3038).

Zhou’s work is supported by Australian Research Council.

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Qi, L., Ling, C., Tong, X. et al. A smoothing projected Newton-type algorithm for semi-infinite programming. Comput Optim Appl 42, 1–30 (2009). https://doi.org/10.1007/s10589-007-9117-x

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  • DOI: https://doi.org/10.1007/s10589-007-9117-x

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