Neural networks for solving systems of linear equations. II. Minimax and least absolute value problems

For pt.I see ibid., vol.39, no.2, p.124-38 (1992). The minimax ( L_∞- 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 the problems to be mapped into systems of nonlinear ordinary differential equations. On the basis of these systems of equations, analog neuronlike 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 architectures are illustrated by extensive computer simulations and CMOS implementations of a general-purpose network architecture are considered