Control Liapunov function design of neural networks that solve convex optimization and variational inequality problems

Authors:
Fernando A. Pazos;Amit Bhaya
Affiliations:
Department of Electrical Engineering, Federal University of Rio de Janeiro, PEE/COPPE/UFRJ, PO Box 68504, Rio de Janeiro 21945-970, Brazil;Department of Electrical Engineering, Federal University of Rio de Janeiro, PEE/COPPE/UFRJ, PO Box 68504, Rio de Janeiro 21945-970, Brazil
Venue:
Neurocomputing
Year:
2009

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Abstract

This paper presents two neural networks to find the optimal point in convex optimization problems and variational inequality problems, respectively. The domain of the functions that define the problems is a convex set, which is determined by convex inequality constraints and affine equality constraints. The neural networks are based on gradient descent and exact penalization and the convergence analysis is based on a control Liapunov function analysis, since the dynamical system corresponding to each neural network may be viewed as a so-called variable structure closed loop control system.