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On smooth reformulations and direct non-smooth computations for minimax problems

Author

Listed:
  • Ralph Kearfott
  • Sowmya Muniswamy
  • Yi Wang
  • Xinyu Li
  • Qian Wang

Abstract

Minimax problems can be approached by reformulating them into smooth problems with constraints or by dealing with the non-smooth objective directly. We focus on verified enclosures of all globally optimal points of such problems. In smooth problems in branch and bound algorithms, interval Newton methods can be used to verify existence and uniqueness of solutions, to be used in eliminating regions containing such solutions, and point Newton methods can be used to obtain approximate solutions for good upper bounds on the global optimum. We analyze smooth reformulation approaches, show weaknesses in them, and compare reformulation to solving the non-smooth problem directly. In addition to analysis and illustrative problems, we exhibit the results of numerical computations on various test problems. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Ralph Kearfott & Sowmya Muniswamy & Yi Wang & Xinyu Li & Qian Wang, 2013. "On smooth reformulations and direct non-smooth computations for minimax problems," Journal of Global Optimization, Springer, vol. 57(4), pages 1091-1111, December.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:4:p:1091-1111
    DOI: 10.1007/s10898-012-0014-1
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    Citations

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    Cited by:

    1. Hermann Schichl & Mihály Markót & Arnold Neumaier, 2014. "Exclusion regions for optimization problems," Journal of Global Optimization, Springer, vol. 59(2), pages 569-595, July.
    2. Ralph Kearfott, 2015. "Some observations on exclusion regions in branch and bound algorithms," Journal of Global Optimization, Springer, vol. 62(2), pages 229-241, June.
    3. Ralph Kearfott, 2014. "On rigorous upper bounds to a global optimum," Journal of Global Optimization, Springer, vol. 59(2), pages 459-476, July.

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