This article is cited in 3 papers

Dual multiplicative algorithms for an entropy-linear programming problem

E. V. Gasnikova

Moscow Institute of Physics and Technology (State University), per. Institutskii 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

Abstract: A multiplicative-barrier generalization of the Cauchy gradient descent method is proposed and studied. The technique is used to search for dual variables in the entropy maximization problem with affine constraints, which arises, for example, in the simulation of equilibria in macroscopic systems. For this class of problems, the dual variables can be used to effectively determine the primal ones. The global convergence of the iterative algorithms proposed is proved.

Key words: multiplicative-barrier iterative algorithms, entropy-linear programming problem, dual problem, Lyapunov's indirect method, Lyapunov's direct method.

UDC: 519.852

Received: 17.07.2007
Revised: 28.10.2008

 English version: Computational Mathematics and Mathematical Physics, 2009, 49:3, 439–449

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