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An inexact primal-dual algorithm for semi-infinite programming

Author

Listed:
  • Bo Wei

    (National University of Singapore)

  • William B. Haskell

    (Purdue University)

  • Sixiang Zhao

    (Shanghai Jiao Tong University)

Abstract

This paper considers an inexact primal-dual algorithm for semi-infinite programming (SIP) for which it provides general error bounds. We create a new prox function for nonnegative measures for the dual update, and it turns out to be a generalization of the Kullback-Leibler divergence. We show that, with a tolerance for small errors (approximation and regularization error), this algorithm achieves an $${\mathcal {O}}(1/\sqrt{K})$$O(1/K) rate of convergence in terms of the optimality gap and constraint violation, where K is the total number of iterations. We then use our general error bounds to analyze the convergence and sample complexity of a specific primal-dual SIP algorithm based on Monte Carlo sampling. Finally, we provide numerical experiments to demonstrate the performance of this algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:91:y:2020:i:3:d:10.1007_s00186-019-00698-2
    DOI: 10.1007/s00186-019-00698-2
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    References listed on IDEAS

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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.
    2. 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.

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