Dual operations on saddle functions

Author:
L. McLinden

Journal:
Trans. Amer. Math. Soc. **179** (1973), 363-381

MSC:
Primary 90C25

DOI:
https://doi.org/10.1090/S0002-9947-1973-0316097-1

MathSciNet review:
0316097

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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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1973-0316097-1

Keywords:
Convex analysis,
minimax theory,
constrained concave-convex problems,
dual extremum problems,
conjugate saddle functions,
equivalence classes,
dual operations,
addition,
extremal convolution,
composition with linear transformations,
subdifferential formulas,
duality formulas,
stability of solutions,
separable saddle functions

Article copyright:
© Copyright 1973
American Mathematical Society