ISSN:
1573-2878
Keywords:
Convexity
;
limiting Lagrangian
;
Lagrangian duality
;
minimax problems
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We show that duality gaps can be closed under broad hypotheses in minimax problems, provided certain changes are made in the maximum part which increase its value. The primary device is to add a linear perturbation to the saddle function, and send it to zero in the limit. Suprema replace maxima, and infima replace minima. In addition to the usual convexity-concavity type of assumptions on the saddle function and the sets, a form of semireflectivity is required for one of the two spaces of the saddle function. A sharpening of the results is possible when one of the spaces is finite-dimensional. A variant of the proof of the previous results leads to a generalization of a result of Sion, from which the theorem of Kneser and Fan follows.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00934766
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