Eprints of Rényi Institute

Using multiobjective optimization to map the entropy region of four random variables

Csirmaz, László (2013) Using multiobjective optimization to map the entropy region of four random variables. Journal of Global Optimization . ISSN 0925-5001 (Submitted)

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Abstract

This paper describes an improved version of Benson's algorithm which finds all vertices of the Pareto set of a multiobjective optimization program. The improved algorithm invokes the LP solver for each vertex and each facet of the Pareto set exactly once, thus reducing the running time significantly. The algorithm was used to generate all extremal consequences of a set of Shannon inequalities for a large set of random variables in order to map the four-variable entropy region. As we were interested in exact solutions, special care was taken for numerical stability. Experimental results demonstrate the viability of the method for determining the Pareto set for medium to large, numerically ill-posed optimization problems.

Item Type:Article
Keywords and phrases:multiobjective programming, effective solutions, entropy region, Benson's algorithm
Subjects:90C05 Linear programming
90C60 Abstract computational complexity for mathematical programming problems
94A17 Measures of information, entropy
Divisions:Research Groups > Theoretical cryptography
Last Modified:02 Mar 2013 20:42

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