Abstract. The paper is devoted to the 75th anniversary of the Kyiv mathematician Naum Shor and is focused on his three central ideas: generalized gradient descent (1962), the use of linear nonorthogonal space transformations to improve the conditionality of ravine-like functions (1969), and dual approach for finding bounds of the objective function in nonconvex quadratic models (1985). Examples of the application of these ideas in methods and algorithms developed at the V.M. Glushkov Institute of Cybernetics of NAS of Ukraine are given. Refs: 32 titles.

Keywords: nondifferentiable optimization, subgradient method, space dilation operator, ellipsoid method, r-algorithm, quadratic extremum problem, dual estimate, functionally redundant constraints.