Subgradient Methods
Main article: Subgradient method See also: Ellipsoid method, Linear programming, Convex optimization, Computational complexity, and Iterative methodN. Z. Shor is well known for his 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. 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.
Read more about this topic: Naum Z. Shor
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