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A Smoothing Newton Method for Semi-Infinite Programming

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Abstract

This paper is concerned with numerical methods for solving a semi-infinite programming problem. We reformulate the equations and nonlinear complementarity conditions of the first order optimality condition of the problem into a system of semismooth equations. By using a perturbed Fischer–Burmeister function, we develop a smoothing Newton method for solving this system of semismooth equations. An advantage of the proposed method is that at each iteration, only a system of linear equations is solved. We prove that under standard assumptions, the iterate sequence generated by the smoothing Newton method converges superlinearly/quadratically.

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Authors and Affiliations

  1. Department of Applied Mathematics, Hunan University Changsha, China

    Dong-Hui Li & Soon-Yi Wu

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Liqun Qi & Judy Tam

Authors
  1. Dong-Hui Li
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  2. Liqun Qi
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  3. Judy Tam
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  4. Soon-Yi Wu
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Li, DH., Qi, L., Tam, J. et al. A Smoothing Newton Method for Semi-Infinite Programming. J Glob Optim 30, 169–194 (2004). https://doi.org/10.1007/s10898-004-8266-z

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  • DOI: https://doi.org/10.1007/s10898-004-8266-z

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