A new geometric condition for Fenchel's duality in infinite dimensional spaces

@article{Burachik2005ANG,
  title={A new geometric condition for Fenchel's duality in infinite dimensional spaces},
  author={Regina Sandra Burachik and Vaithilingam Jeyakumar},
  journal={Math. Program.},
  year={2005},
  volume={104},
  pages={229-233}
}
In 1951, Fenchel discovered a special duality, which relates the minimization of a sum of two convex functions with the maximization of the sum of concave functions, using conjugates. Fenchel’s duality is central to the study of constrained optimization. It requires an existence of an interior point of a convex set which often has empty interior in optimization applications. The well known relaxations of this requirement in the literature are again weaker forms of the interior point condition… CONTINUE READING

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