Subgradient and ε-Subgradient Methods

  • Naum Z. Shor
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 24)


Let us consider a convex programming problem (CPP):
$$find{f^*} = \inf {f_0}\left( x \right),x = \left( {{x^{\left( 1 \right)}},...,{x^{\left( n \right)}}} \right) \in {E^n},$$
subject to constraints:
$${f_i}\left( x \right)\quad 0,\quad i \in \left\{ {1,2, \ldots ,m} \right\} = I;$$
$$x \in X\quad \subseteq {E^n},$$
where F ν (x), ν ∈ {{0} ∪ I}, are proper convex fuctions determined on convex open neigborhood X 1 of a given convex set X. We introduce the notion of “information portion” for this problem.


Convex Function Steep Descent Method Bundle Method Subgradient Method Convex Programming Problem 
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

  • Naum Z. Shor
    • 1
  1. 1.V.M. Glushkov Institute of CyberneticsUkrainian National Academy of SciencesKievUkraine

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