Advances in Economic Theory: On the complexity of linear programming

This is a partial survey of results on the complexity of the linear programming problem since the ellipsoid method. The main topics are polynomial and strongly polynomial algorithms, probabilistic analysis of simplex algorithms, and recent interior point methods.

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[79]  Michael A. Saunders,et al.  On projected newton barrier methods for linear programming and an equivalence to Karmarkar’s projective method , 1986, Math. Program..

[80]  Earl R. Barnes,et al.  A variation on Karmarkar’s algorithm for solving linear programming problems , 1986, Math. Program..

[81]  Nimrod Megiddo,et al.  On the expected number of linear complementarity cones intersected by random and semi-random rays , 1986, Math. Program..

[82]  Richard M. Karp,et al.  A Family of Simplex Variants Solving an m × d Linear Program in Expected Number of Pivot Steps Depending on d Only , 1986, Math. Oper. Res..

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[95]  Richard M. Karp,et al.  A simplex variant solving an m times d linear program in O(min(m2, d2) expected number of pivot steps , 1987, J. Complex..

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