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On the Use of Augmented Lagrangians in the Solution of Generalized Semi-Infinite Min-Max Problems

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Abstract

We present an approach for the solution of a class of generalized semi-infinite optimization problems. Our approach uses augmented Lagrangians to transform generalized semi-infinite min-max problems into ordinary semi-infinite min-max problems, with the same set of local and global solutions as well as the same stationary points. Once the transformation is effected, the generalized semi-infinite min-max problems can be solved using any available semi-infinite optimization algorithm. We illustrate our approach with two numerical examples, one of which deals with structural design subject to reliability constraints.

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, 94720, USA

    Elijah Polak (Emeritus Professor)

  2. Department of Operations Research, Naval Postgraduate School, 239 Glasgow Hall, Monterey, CA, 93943, USA

    Johannes O. Royset (Research Associate)

Authors
  1. Elijah Polak
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  2. Johannes O. Royset
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Correspondence to Johannes O. Royset.

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Polak, E., Royset, J.O. On the Use of Augmented Lagrangians in the Solution of Generalized Semi-Infinite Min-Max Problems. Comput Optim Applic 31, 173–192 (2005). https://doi.org/10.1007/s10589-005-2179-8

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  • DOI: https://doi.org/10.1007/s10589-005-2179-8

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