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A smoothing Levenberg–Marquardt algorithm for semi-infinite programming

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  • Ping Jin
  • Chen Ling
  • Huifei Shen

Abstract

In this paper, we present a smoothing Levenberg–Marquardt algorithm for the solution of the semi-infinite programming (SIP) problem. We first reformulate the KKT system of SIP problem into a system of constrained nonsmooth equations. Then we solve this system by a smoothing Levenberg–Marquardt algorithm. The feasibility is ensured via the aggregated constraint, and at each iteration of the presented algorithm only a quadratic programming has to be solved. Global and local superlinear convergence of this algorithm is established under a local error bound condition, which is much weaker than the nonsingularity condition. Preliminary numerical results are reported. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Ping Jin & Chen Ling & Huifei Shen, 2015. "A smoothing Levenberg–Marquardt algorithm for semi-infinite programming," Computational Optimization and Applications, Springer, vol. 60(3), pages 675-695, April.
    • Handle: RePEc:spr:coopap:v:60:y:2015:i:3:p:675-695
    DOI: 10.1007/s10589-014-9698-0
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    References listed on IDEAS

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    1. C. Ling & L. Q. Qi & G. L. Zhou & S. Y. Wu, 2006. "Global Convergence of a Robust Smoothing SQP Method for Semi-Infinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 147-164, April.
    2. S. Ito & Y. Liu & K.L. Teo, 2000. "A Dual Parametrization Method for Convex Semi-Infinite Programming," Annals of Operations Research, Springer, vol. 98(1), pages 189-213, December.
    3. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    4. Chen Ling & Qin Ni & Liqun Qi & Soon-Yi Wu, 2010. "A new smoothing Newton-type algorithm for semi-infinite programming," Journal of Global Optimization, Springer, vol. 47(1), pages 133-159, May.
    5. Dong-Hui Li & Liqun Qi & Judy Tam & Soon-Yi Wu, 2004. "A Smoothing Newton Method for Semi-Infinite Programming," Journal of Global Optimization, Springer, vol. 30(2), pages 169-194, November.
    6. K.L. Teo & X.Q. Yang & L.S. Jennings, 2000. "Computational Discretization Algorithms for Functional Inequality Constrained Optimization," Annals of Operations Research, Springer, vol. 98(1), pages 215-234, December.
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    Cited by:

    1. Bo Wei & William B. Haskell & Sixiang Zhao, 2020. "The CoMirror algorithm with random constraint sampling for convex semi-infinite programming," Annals of Operations Research, Springer, vol. 295(2), pages 809-841, December.

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