Neural Networks for Solving Systems of Linear Equations—Part II: Minimax and Least Absolute Value Problems

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Abstract

The minimax (Lx-or Chebyshev norm) and the least absolute value (L1-norm) optimization criteria for linear parameter estimation problems are reformulated as constrained minimization problems. For these problems appropriate energy (Lyapunov) functions are constructed which enable us to map the problems into systems of nonlinear ordinary differential equations. On the basis of these systems of equations new analog neuron-like network architectures are proposed and their properties are discussed. The proposed circuit structures exhibit a high degree of modularity, and in most cases a relatively small number of basic building blocks (processing units) are required to implement effective and powerful optimization algorithms. The validity and performance of the proposed neural network architectures are illustrated by extensive computer simulations.

Original languageEnglish
Pages (from-to)619-633
Number of pages15
JournalIEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing
Volume39
Issue number9
DOIs
Publication statusPublished - Sep 1992
Externally publishedYes

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