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An Interior Point Constraint Generation Algorithm for Semi-Infinite Optimization with Health-Care Application

Author

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  • Mohammad R. Oskoorouchi

    (College of Business Administration, California State University, San Marcos, San Marcos, California 92096)

  • Hamid R. Ghaffari

    (Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada)

  • Tamás Terlaky

    (Department Industrial and Systems Engineering, Lehigh University, Bethlehem, Pennsylvania 18015)

  • Dionne M. Aleman

    (Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada)

Abstract

We propose an interior point constraint generation (IPCG) algorithm for semi-infinite linear optimization (SILO) and prove that the algorithm converges to an (epsilon)-solution of SILO after a finite number of constraints is generated. We derive a complexity bound on the number of Newton steps needed to approach the updated (mu)-center after adding multiple violated constraints and a complexity bound on the total number of constraints that is required for the overall algorithm to converge.We implement our algorithm to solve the sector duration optimization problem arising in Leksell Gamma Knife® Perfexion™ (Elekta, Stockholm Sweden) treatment planning, a highly specialized treatment for brain tumors. Using real patient data provided by the Department of Radiation Oncology at Princess Margaret Hospital in Toronto, Ontario, Canada, we show that our algorithm can efficiently handle problems in real-life health-care applications by providing a quality treatment plan in a timely manner.Comparing our computational results with MOSEK, a commercial software package, we show that the IPCG algorithm outperforms the classical primal-dual interior point methods on sector duration optimization problem arising in Perfexion™ treatment planning. We also compare our results with that of a projected gradient method. In both cases we show that IPCG algorithm obtains a more accurate solution substantially faster.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:5:p:1184-1197
    DOI: 10.1287/opre.1110.0951
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    References listed on IDEAS

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    Cited by:

    1. Csaba Fábián & Olga Papp & Krisztián Eretnek, 2013. "Implementing the simplex method as a cutting-plane method, with a view to regularization," Computational Optimization and Applications, Springer, vol. 56(2), pages 343-368, October.
    2. M. A. Goberna & M. A. López, 2017. "Recent contributions to linear semi-infinite optimization," 4OR, Springer, vol. 15(3), pages 221-264, September.
    3. Oylum S¸eker & Mucahit Cevik & Merve Bodur & Young Lee & Mark Ruschin, 2023. "A Multiobjective Approach for Sector Duration Optimization in Stereotactic Radiosurgery Treatment Planning," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 248-264, January.
    4. Amir Ahmadi-Javid & Nasrin Ramshe, 2019. "Designing flexible loop-based material handling AGV paths with cell-adjacency priorities: an efficient cutting-plane algorithm," 4OR, Springer, vol. 17(4), pages 373-400, December.
    5. M. A. Goberna & M. A. López, 2018. "Recent contributions to linear semi-infinite optimization: an update," Annals of Operations Research, Springer, vol. 271(1), pages 237-278, December.

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