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Relaxed cutting plane method with convexification for solving nonlinear semi-infinite programming problems

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  • Ting-Jang Shiu
  • Soon-Yi Wu

Abstract

In this paper, we present an algorithm to solve nonlinear semi-infinite programming (NSIP) problems. To deal with the nonlinear constraint, Floudas and Stein (SIAM J. Optim. 18:1187–1208, 2007 ) suggest an adaptive convexification relaxation to approximate the nonlinear constraint function. The αBB method, used widely in global optimization, is applied to construct the convexification relaxation. We then combine the idea of the cutting plane method with the convexification relaxation to propose a new algorithm to solve NSIP problems. With some given tolerances, our algorithm terminates in a finite number of iterations and obtains an approximate stationary point of the NSIP problems. In addition, some NSIP application examples are implemented by the method proposed in this paper, such as the proportional-integral-derivative controller design problem and the nonlinear finite impulse response filter design problem. Based on our numerical experience, we demonstrate that our algorithm enhances the computational speed for solving NSIP problems. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Ting-Jang Shiu & Soon-Yi Wu, 2012. "Relaxed cutting plane method with convexification for solving nonlinear semi-infinite programming problems," Computational Optimization and Applications, Springer, vol. 53(1), pages 91-113, September.
    • Handle: RePEc:spr:coopap:v:53:y:2012:i:1:p:91-113
    DOI: 10.1007/s10589-011-9452-9
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    References listed on IDEAS

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    1. 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. Mengwei Xu & Soon-Yi Wu & Jane Ye, 2014. "Solving semi-infinite programs by smoothing projected gradient method," Computational Optimization and Applications, Springer, vol. 59(3), pages 591-616, December.
    2. Zhi Guo Feng & Fei Chen & Lin Chen & Ka Fai Cedric Yiu, 2020. "Optimality Analysis of a Class of Semi-infinite Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 398-411, August.

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