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

Authors:
Elijah Polak;Johannes O. Royset
Affiliations:
Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, USA 94720;Department of Operations Research, Naval Postgraduate School, Monterey, USA 93943
Venue:
Computational Optimization and Applications
Year:
2005

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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.