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Cybernetics and Systems Analysis

, Volume 48, Issue 1, pp 2–16 | Cite as

On N. Z. Shor’s three scientific ideas

  • I. V. SergienkoEmail author
  • P. I. Stetsyuk
Article

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 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 the NAS of Ukraine are given.

Keywords

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

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Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.V.M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

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