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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Conjugacy correspondences: a unified view


Author: L. McLinden
Journal: Trans. Amer. Math. Soc. 203 (1975), 257-274
MSC: Primary 49A25; Secondary 46G99
MathSciNet review: 0365276
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Abstract: As preparation for a duality theory for saddle programs, a partial conjugacy correspondence is developed among equivalence classes of saddle functions. Three known conjugacy correspondences, including Fenchel's correspondence among convex functions and Rockafellar's extension of it to equivalence classes of saddle functions, are shown to be degenerate special cases. Additionally, two new correspondences are brought to light as further special cases. Various questions are answered concerning the lower and upper closures and effective domain of the resulting equivalence class, as well as the effect the correspondence has on the related purely convex function and the subdifferential mapping.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0365276-8
Keywords: Convex analysis, conjugacy correspondences, minimax theory, saddle programs, duality, conjugate saddle functions, equivalence classes, closure formulas, subdifferential formulas
Article copyright: © Copyright 1975 American Mathematical Society