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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- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 203 (1975), 257-274
- MSC: Primary 49A25; Secondary 46G99
- DOI: https://doi.org/10.1090/S0002-9947-1975-0365276-8
- MathSciNet review: 0365276