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Relaxed Cutting Plane Method for Solving Linear Semi-Infinite Programming Problems

Author

Listed:
  • S. Y. Wu

    (National Cheng Kung University)

  • S. C. Fang

    (North Carolina State University)

  • C. J. Lin

    (University of Michigan)

Abstract

One of the major computational tasks of using the traditional cutting plane approach to solve linear semi-infinite programming problems lies in finding a global optimizer of a nonlinear and nonconvex program. This paper generalizes the Gustafson and Kortanek scheme to relax this requirement. In each iteration, the proposed method chooses a point at which the infinite constraints are violated to a degree, rather than a point at which the violations are maximized. A convergence proof of the proposed scheme is provided. Some computational results are included. An explicit algorithm which allows the unnecessary constraints to be dropped in each iteration is also introduced to reduce the size of computed programs.

Suggested Citation

  • S. Y. Wu & S. C. Fang & C. J. Lin, 1998. "Relaxed Cutting Plane Method for Solving Linear Semi-Infinite Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 99(3), pages 759-779, December.
    • Handle: RePEc:spr:joptap:v:99:y:1998:i:3:d:10.1023_a:1021763419562
    DOI: 10.1023/A:1021763419562
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    Citations

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    Cited by:

    1. Mohammad R. Oskoorouchi & Hamid R. Ghaffari & Tamás Terlaky & Dionne M. Aleman, 2011. "An Interior Point Constraint Generation Algorithm for Semi-Infinite Optimization with Health-Care Application," Operations Research, INFORMS, vol. 59(5), pages 1184-1197, October.
    2. Fang, S-C. & Wu, S. & Birbil, S.I., 2002. "Solving variational inequalities defined on a domain with infinitely many linear constraints," Econometric Institute Research Papers EI 2002-51, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Ralf Werner, 2008. "Cascading: an adjusted exchange method for robust conic programming," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 179-189, June.
    4. Li-Ping Pang & Jian Lv & Jin-He Wang, 2016. "Constrained incremental bundle method with partial inexact oracle for nonsmooth convex semi-infinite programming problems," Computational Optimization and Applications, Springer, vol. 64(2), pages 433-465, June.
    5. 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.
    6. Fang, S-C. & Wu, S. & Birbil, S.I., 2002. "Solving Variational Inequalities Defined on A Domain with Infinitely Many Linear Constraints," ERIM Report Series Research in Management ERS-2002-70-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    7. Soren Christensen, 2011. "A method for pricing American options using semi-infinite linear programming," Papers 1103.4483, arXiv.org, revised Jun 2011.
    8. C.F. Wen & S.Y. Wu, 2004. "Duality theorems and algorithms for linear programming in measure spaces," Journal of Global Optimization, Springer, vol. 30(2), pages 207-233, November.

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