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Near-optimal solutions of convex semi-infinite programs via targeted sampling

Author

Listed:
  • Souvik Das

    (Indian Institute of Technology Bombay)

  • Ashwin Aravind

    (Indian Institute of Technology Bombay)

  • Ashish Cherukuri

    (University of Groningen)

  • Debasish Chatterjee

    (Indian Institute of Technology Bombay)

Abstract

We propose an approach to find the optimal value of a convex semi-infinite program (SIP) that involves identifying a finite set of relevant constraints by solving a finite-dimensional global maximization problem. One of the major advantages of our approach is that it admits a plug-and-play module where any suitable global optimization algorithm can be employed to obtain the optimal value of the SIP. As an example, we propose a simulated annealing based algorithm which is useful especially when the constraint index set is high-dimensional. A proof of convergence of the algorithm is included, and the performance and accuracy of the algorithm itself are illustrated on several benchmark SIPs lifted from the literature.

Suggested Citation

  • Souvik Das & Ashwin Aravind & Ashish Cherukuri & Debasish Chatterjee, 2022. "Near-optimal solutions of convex semi-infinite programs via targeted sampling," Annals of Operations Research, Springer, vol. 318(1), pages 129-146, November.
    • Handle: RePEc:spr:annopr:v:318:y:2022:i:1:d:10.1007_s10479-022-04810-4
    DOI: 10.1007/s10479-022-04810-4
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    References listed on IDEAS

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    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.
    2. Bruce Hajek, 1988. "Cooling Schedules for Optimal Annealing," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 311-329, May.
    3. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    4. 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.
    5. Bo Wei & William B. Haskell & Sixiang Zhao, 2020. "An inexact primal-dual algorithm for semi-infinite programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 501-544, June.
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