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Global Convergence of a Robust Smoothing SQP Method for Semi-Infinite Programming

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Abstract

The semi-infinite programming (SIP) problem is a program with infinitely many constraints. It can be reformulated as a nonsmooth nonlinear programming problem with finite constraints by using an integral function. Due to the nondifferentiability of the integral function, gradient-based algorithms cannot be used to solve this nonsmooth nonlinear programming problem. To overcome this difficulty, we present a robust smoothing sequential quadratic programming (SQP) algorithm for solving the nonsmooth nonlinear programming problem. At each iteration of the algorthm, we need to solve only a quadratic program that is always feasible and solvable. The global convergence of the algorithm is established under mild conditions. Numerical results are given.

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Authors and Affiliations

  1. School of Information, Zhejiang University of Finance and Economics, Hangzhou, China

    C. Ling (Professor)

  2. Department of Mathematics, City University of Hong Kong, Kowloon Tong, Kowloon, Hong Kong

    L. Q. Qi (Chair Professor)

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

    G. L. Zhou (Senior Lecturer)

  4. Institute of Applied Mathematics, National Cheng-Kung University, Tainan, Taiwan

    S. Y. Wu (Professor)

Authors
  1. C. Ling
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  2. L. Q. Qi
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  3. G. L. Zhou
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  4. S. Y. Wu
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Additional information

Communicated by F. Giannessi

His work was supported by the Hong Kong Research Grant Council

His work was supported by the Australian Research Council.

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Ling, C., Qi, L.Q., Zhou, G.L. et al. Global Convergence of a Robust Smoothing SQP Method for Semi-Infinite Programming. J Optim Theory Appl 129, 147–164 (2006). https://doi.org/10.1007/s10957-006-9049-0

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  • DOI: https://doi.org/10.1007/s10957-006-9049-0

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