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On the Use of Outer Approximations as an External Active Set Strategy

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  • H. Chung

    (University of California)

  • E. Polak

    (University of California)

  • S. Sastry

    (University of California)

Abstract

Outer approximations are a well known technique for solving semiinfinite optimization problems. We show that a straightforward adaptation of this technique results in a new, external, active-set strategy that can easily be added to existing software packages for solving nonlinear programming problems with a large number of inequality constraints. Our external active-set strategy is very easy to implement, and, as our numerical results show, it is particularly effective when applied to discretized semiinfinite optimization or state-constrained optimal control problems. Its effects can be spectacular, with reductions in computing time that become progressively more pronounced as the number of inequalities is increased.

Suggested Citation

  • H. Chung & E. Polak & S. Sastry, 2010. "On the Use of Outer Approximations as an External Active Set Strategy," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 51-75, July.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:1:d:10.1007_s10957-010-9655-8
    DOI: 10.1007/s10957-010-9655-8
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    References listed on IDEAS

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    1. E. Polak & R. S. Womersley & H. X. Yin, 2008. "An Algorithm Based on Active Sets and Smoothing for Discretized Semi-Infinite Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 311-328, August.
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    Cited by:

    1. L. Jeff Hong & Zhaolin Hu & Liwei Zhang, 2014. "Conditional Value-at-Risk Approximation to Value-at-Risk Constrained Programs: A Remedy via Monte Carlo," INFORMS Journal on Computing, INFORMS, vol. 26(2), pages 385-400, May.

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