Dual operations on saddle functions

McLinden, L.

doi:10.1090/S0002-9947-1973-0316097-1

Dual operations on saddle functions
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Trans. Amer. Math. Soc. 179 (1973), 363-381 Request permission

Abstract:

Dual operations on convex functions play a central role in the analysis of constrained convex optimization problems. Our aim here is to provide tools for a similar analysis of constrained concave-convex minimax problems. Two pairs of dual operations on convex functions, including addition and infimal convolution, are extended to saddle functions. For the resulting saddle functions much detailed information is given, including subdifferential formulas. Also, separable saddle functions are defined and some basic facts about them established.

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