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Naum Zuselevich Shor ((ロシア語:Шор Наум Зуселевич)) (1 January 1937 – 26 February 2006) was a Soviet and Ukrainian Jewish mathematician specializing in optimization. He made significant contributions to nonlinear and stochastic programming, numerical techniques for non-smooth optimization, discrete optimization problems, matrix optimization, dual quadratic bounds in multi-extremal programming problems. Shor became a full member of the National Academy of Science of Ukraine in 1998. ==Subgradient methods== (詳細はmethod of generalized gradient descent with space dilation in the direction of the difference of two successive subgradients (the so-called r-algorithm), that was created in collaboration with Nikolay G. Zhurbenko.〔N. Z. Shor and N. G. Zhurbenko, "The minimization method using space dilatation in direction of difference of two sequential gradients," Kibernetika, No. 3, 51-59 (1971).〕〔 Free implementations of r-algorithm (made by workers of Department Methods for solving complex optimization problems led for a long time by N. Z. Shor) are available in * (SolvOpt ) * (ralg ) from OpenOpt framework.〕 The ellipsoid method was re-invigorated by A.S. Nemirovsky and D.B. Yudin, who developed a careful complexity analysis of its approximation properties for problems of convex minimization with real data. However, it was Leonid Khachiyan who provided the rational-arithmetic complexity analysis, using an ellipsoid algorithm, that established that linear programming problems can be solved in polynomial time. It has long been known that the ellipsoidal methods are special cases of these subgradient-type methods. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Naum Z. Shor」の詳細全文を読む スポンサード リンク
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