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An Interior-Point Algorithm for Nonlinear Minimax Problems

Author

Listed:
  • E. Obasanjo

    (Barclays Capital)

  • G. Tzallas-Regas

    (Imperial College London)

  • B. Rustem

    (Imperial College London)

Abstract

We present a primal-dual interior-point method for constrained nonlinear, discrete minimax problems where the objective functions and constraints are not necessarily convex. The algorithm uses two merit functions to ensure progress toward the points satisfying the first-order optimality conditions of the original problem. Convergence properties are described and numerical results provided.

Suggested Citation

  • E. Obasanjo & G. Tzallas-Regas & B. Rustem, 2010. "An Interior-Point Algorithm for Nonlinear Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 291-318, February.
    • Handle: RePEc:spr:joptap:v:144:y:2010:i:2:d:10.1007_s10957-009-9599-z
    DOI: 10.1007/s10957-009-9599-z
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    References listed on IDEAS

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    1. I. Akrotirianakis & B. Rustem, 2005. "Globally Convergent Interior-Point Algorithm for Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 125(3), pages 497-521, June.
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    Cited by:

    1. E. Y. Pee & J. O. Royset, 2011. "On Solving Large-Scale Finite Minimax Problems Using Exponential Smoothing," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 390-421, February.
    2. Zhengyong Zhou & Xiaoyang Dai, 2023. "An active set strategy to address the ill-conditioning of smoothing methods for solving finite linear minimax problems," Journal of Global Optimization, Springer, vol. 85(2), pages 421-439, February.
    3. Junxiang Li & Mingsong Cheng & Bo Yu & Shuting Zhang, 2015. "Group Update Method for Sparse Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 257-277, July.
    4. Jin-bao Jian & Xing-de Mo & Li-juan Qiu & Su-ming Yang & Fu-sheng Wang, 2014. "Simple Sequential Quadratically Constrained Quadratic Programming Feasible Algorithm with Active Identification Sets for Constrained Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 158-188, January.

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    1. B. Rustem & S. Žaković & P. Parpas, 2008. "Convergence of an Interior Point Algorithm for Continuous Minimax," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 87-103, January.

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