Given a function f:S →[−∞, +∞] on a set SR n, the sets
$$\begin{array}{*{20}c} {domf = \{ x \in S|f\left( x \right) < + \infty \} } \\ {epif = \{ \left( {x,a} \right) \in S \times R|f\left( x \right) \leqslant \alpha \} } \\ \end{array} $$
are called the effective domain and the epigraph of f (x), respectively. If dom f ≠Ø and f (x) > −∞ for all xS then we say that the function f (x) is proper.


Convex Function Affine Function Lineality Space Convex Envelope Proper Convex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Hoang Tuy
    • 1
  1. 1.Institute of MathematicsHanoiVietnam

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