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Cybernetics and Systems Analysis

, Volume 34, Issue 2, pp 176–184 | Cite as

Construction of convex continuations for functions defined on a hypersphere

  • Yu. G. Stoyan
  • S. V. Yakovlev
  • O. A. Emets
  • O. A. Valuiskaya
Cybernetics

Abstract

Construction of convex continuations for functions defined on the vertices of some combinatorial polyhedra, in particular the permutation polyhedron and the arrangement polyhedron, has been studied in [1, 2]. Subsequently this result has been generalized to functions defined at the extreme points of an arbitrary polyhedron [3]. For purposes of combinatorial optimization [4-6] it is relevant to consider the existence and construction of convex continuations from continua, in particular, when the function is defined on a hypersphere in thek-dimensional space. Unfortunately, passage to the limit from discrete sets to continua does not produce positive results in this case. We are thus forced to develop special approaches to investigating the existence of convex continuations of functions defined on continua.

Keywords

Partial Derivative Quadratic Form Naukova Dumka Real Root Geometrical Design 
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

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • Yu. G. Stoyan
  • S. V. Yakovlev
  • O. A. Emets
  • O. A. Valuiskaya

There are no affiliations available

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