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Combined Entropic Regularization and Path-Following Method for Solving Finite Convex Min-max Problems Subject to Infinitely Many Linear Constraints

Author

Listed:
  • R. L. Sheu

    (National Cheng-Kung University)

  • S. Y. Wu

    (National Cheng-Kung University)

Abstract

In this paper, we study the minimization of the max function of q smooth convex functions on a domain specified by infinitely many linear constraints. The difficulty of such problems arises from the kinks of the max function and it is often suggested that, by imposing certain regularization functions, nondifferentiability will be overcome. We find that the entropic regularization introduced by Li and Fang is closely related to recently developed path-following interior-point methods. Based on their results, we create an interior trajectory in the feasible domain and propose a path-following algorithm with a convergence proof. Our intention here is to show a nice combination of minmax problems, semi-infinite programming, and interior-point methods. Hopefully, this will lead to new applications.

Suggested Citation

  • R. L. Sheu & S. Y. Wu, 1999. "Combined Entropic Regularization and Path-Following Method for Solving Finite Convex Min-max Problems Subject to Infinitely Many Linear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 167-190, April.
    • Handle: RePEc:spr:joptap:v:101:y:1999:i:1:d:10.1023_a:1021727228957
    DOI: 10.1023/A:1021727228957
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    References listed on IDEAS

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    1. Xing-Si Li & Shu-Cherng Fang, 1997. "On the entropic regularization method for solving min-max problems with applications," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(1), pages 119-130, February.
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    Cited by:

    1. Alfred Auslender & Miguel A. Goberna & Marco A. López, 2009. "Penalty and Smoothing Methods for Convex Semi-Infinite Programming," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 303-319, May.

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