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A barrier function method for minimax problems
 E. Polak,
 J. E. Higgins,
 D. Q. Mayne
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This paper presents an algorithm based on barrier functions for solving semiinfinite minimax problems which arise in an engineering design setting. The algorithm bears a resemblance to some of the current interior penalty function methods used to solve constrained minimization problems. Global convergence is proven, and numerical results are reported which show that the algorithm is exceptionally robust, and that its performance is comparable, while its structure is simpler than that of current firstorder minimax algorithms.
This research was supported by the National Science Foundation grant ECS8517362, the Air Force Office Scientific Research grant 860116, the California State MICRO program, and the United Kingdom Science and Engineering Research Council.
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 Title
 A barrier function method for minimax problems
 Journal

Mathematical Programming
Volume 54, Issue 13 , pp 155176
 Cover Date
 19920201
 DOI
 10.1007/BF01586049
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Barrier function methods
 interior penalty methods
 minimax algorithms
 engineering design
 nondifferentiable optimization
 Industry Sectors
 Authors

 E. Polak ^{(1)}
 J. E. Higgins ^{(1)}
 D. Q. Mayne ^{(2)}
 Author Affiliations

 1. Department of Electrical Engineering and Computer Sciences and the Electronics Research Laboratory, University of California, 94720, Berkeley, CA, USA
 2. Department of Electrical Engineering, Imperial College, SW7 2BT, London, UK