The theory of convex extensions in combinatorial optimization problems - Yakovlev, S.V. (Reports of the National Academy of Sciences of Ukraine, 2017)
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.