Boundedness Theorems for the Relaxation Method

Authors:
Edoardo Amaldi;Raphael Hauser
Affiliations:
Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy;Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom
Venue:
Mathematics of Operations Research
Year:
2005

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Abstract

A classical theorem by Block and Levin (Block, H. D., S. A. Levin. 1970. On the boundedness of an iterative procedure for solving a system of linear inequalities. Proc. Amer. Math. Soc.26 229-235) states that certain variants of the relaxation method for solving systems of linear inequalities generate bounded sequences of intermediate solutions, even when applied to infeasible systems. Using a new approach, we prove a more general version of this result and answer an old open problem of quantifying the bound as a function of the input data.