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求解线性规划的多项式时间算法

A Polynomial-Time Algorithm for Solving Linear Programs

Mathematics of Operations Research · 1980
被引 0
ABS 3

中文导读

苏联数学家Khachiyan证明了线性规划可以通过椭球算法的变体在多项式时间内求解,这是理论上的重大突破。

Abstract

A young Russian mathematician, Leonid G. Khachiyan, has made a stunning theoretical breakthrough (Khachiyan, L. 1979. A polynomial algorithm in linear programming. Dokl. Akad. Nauk SSSR 224 1093–1096. [English translation in Soviet Math. Dokl. 20 191–194.]) by showing that linear programs can indeed be solved in polynomial time by a variant of an iterative ellipsoidal algorithm developed by N. Z. Shor (Shor, N. 1977. Cut-off method with space extension in convex programming problems. Kibernetika 13 94–95. [English translation in Cybernetics 13 94–96.]).

线性规划多项式时间算法椭球算法数学优化