An Introduction to Abstract Convexity

  • Alexander Rubinov
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 44)

Abstract

One of the main results of convex analysis states that an arbitrary lower semicontinuous convex function f (perhaps admitting the value +∞) is the upper envelope of the set of all its affine minorants:
$$f\left( x \right) = \sup \left\{ {h\left( x \right):h\;is\;an\;affine\;function,\;h \leqslant f} \right\}$$
.

Keywords

Convex Function Coupling Function Separation Property Affine Function Vertical Shift 
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 2000

Authors and Affiliations

  • Alexander Rubinov
    • 1
  1. 1.School of Information Technology and Mathematical SciencesUniversity of BallaratVictoriaAustralia

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