A Polynomial-time Rescaling Algorithm for Solving Linear Programs

We show that the perceptron algorithm along with periodic rescaling solves linear programs in polynomial time. The algorithm requires no matrix inversions and no barrier functions.

[1]  A. A. Mullin,et al.  Principles of neurodynamics , 1962 .

[2]  John Dunagan,et al.  Smoothed analysis of the perceptron algorithm for linear programming , 2002, SODA '02.

[3]  Santosh S. Vempala,et al.  Solving convex programs by random walks , 2002, STOC '02.

[4]  Pravin M. Vaidya,et al.  A new algorithm for minimizing convex functions over convex sets , 1989, 30th Annual Symposium on Foundations of Computer Science.

[5]  L. G. H. Cijan A polynomial algorithm in linear programming , 1979 .

[6]  Rocco A. Servedio,et al.  On PAC learning using Winnow, Perceptron, and a Perceptron-like algorithm , 1999, COLT '99.

[7]  Tom Bylander,et al.  Learning linear threshold functions in the presence of classification noise , 1994, COLT '94.

[8]  John N. Tsitsiklis,et al.  Introduction to linear optimization , 1997, Athena scientific optimization and computation series.

[9]  D. Spielman,et al.  Smoothed Analysis of Renegar’s Condition Number for Linear Programming , 2002 .

[10]  James Renegar,et al.  Incorporating Condition Measures into the Complexity Theory of Linear Programming , 1995, SIAM J. Optim..

[11]  Jürgen Forster A linear lower bound on the unbounded error probabilistic communication complexity , 2002, J. Comput. Syst. Sci..

[12]  Marvin Minsky,et al.  Perceptrons: An Introduction to Computational Geometry , 1969 .

[13]  Pravin M. Vaidya,et al.  A new algorithm for minimizing convex functions over convex sets , 1996, Math. Program..

[14]  L. Lovász,et al.  Geometric Algorithms and Combinatorial Optimization , 1981 .

[15]  Felipe Cucker,et al.  A new condition number for linear programming , 2001, Math. Program..

[16]  Rocco A. Servedio,et al.  Smooth boosting and learning with malicious noise , 2003 .

[17]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, STOC '84.

[18]  Alan M. Frieze,et al.  A Polynomial-Time Algorithm for Learning Noisy Linear Threshold Functions , 1996, Algorithmica.