The theory of convex extensions in combinatorial optimization problems

1Yakovlev, SV
1National Aerospace University "Zhukovskiy Kharkiv Aviation Institute"
Dopov. Nac. akad. nauk Ukr. 2017, 8:20-26
Section: Information Science and Cybernetics
Language: Russian

The results of the theory of convex extensions for vertex located and polyhedral-spherical sets are summarized. In view of the theorems of existence of convex differentiable extensions, the problem is equivalent to a discrete optimization problem of convex functions under convex functional constraints. The convex nonlinear relaxation problem is considered.

Keywords: combinatorial optimization, combinatorial polyhedron, convex extension, vertex located set
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