Efficient recurrent neural network model for the solution of general nonlinear optimization problems

Authors:
A. Malek;N. Hosseinipour-Mahani;S. Ezazipour
Affiliations:
Department of Applied Mathematics, Tarbiat Modares University, Tehran, Iran;Department of Applied Mathematics, Tarbiat Modares University, Tehran, Iran;Department of Applied Mathematics, Tarbiat Modares University, Tehran, Iran
Venue:
Optimization Methods & Software
Year:
2010

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Abstract

In this paper, we propose a projection neural network model for solving nonlinear convex optimization problems with general linear constraints. Compared with the existing neural network models for solving nonlinear optimization problems, the proposed neural network can be applied to solve a broad class of constrained optimization problems such as degenerate, saddle point, and quadratic problems. It is shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent. This model is exponentially stable. Simulation results are given to illustrate the global convergence and performance of the proposed model for various classes of constrained optimization problems. Both theoretical and numerical approaches are considered. Numerical results are in good agreement with the proved theoretical concepts.