The scientific heritage of Academician Shor

An overview of the scientific heritage of Academician N.Z. Shor is provided. His fundamental scientific ideas are considered, including the method of sequential analysis of variants (1961), subgradient method (1962), the use of linear non-orthogonal space transformations for improving the properties of ravine functions (1969), and a dual approach for obtaining and refining objective function estimates in non-convex quadratic models (1985). Examples of implementing these ideas in the methods and algorithms developed at the V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine are presented. Keywords: non-smooth (non-differentiable) function, subgradient method, space dilation operator, ellipsoid method, r-algorithm, extremal quadratic problem.