Novel artificial neural network with simulation aspects for solving linear and quadratic programming problems

Authors:
H. Ghasabi-Oskoei;A. Malek;A. Ahmadi
Affiliations:
Mathematics and Informatics Research Group, Academic Center for Education, Culture and Research, Tarbiat Modarres University, P.O. Box 14115-343, Tehran, Iran;Department of Mathematics, Tarbiat Modarres University, P.O. Box 14115-175, Tehran, Iran;Mathematics and Informatics Research Group, Academic Center for Education, Culture and Research, Tarbiat Modarres University, P.O. Box 14115-343, Tehran, Iran
Venue:
Computers & Mathematics with Applications
Year:
2007

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Abstract

In this paper linear and quadratic programming problems are solved using a novel recurrent artificial neural network. The new model is simpler and converges very fast to the exact primal and dual solutions simultaneously. The model is based on a nonlinear dynamical system, using arbitrary initial conditions. In order to construct an economy model, here we avoid using analog multipliers. The dynamical system is a time dependent system of equations with the gradient of specific Lyapunov energy function in the right hand side. Block diagram of the proposed neural network model is given. Fourth order Runge-Kutta method with controlled step size is used to solve the problem numerically. Global convergence of the new model is proved, both theoretically and numerically. Numerical simulations show the fast convergence of the new model for the problems with a unique solution or infinitely many. This model converges to the exact solution independent of the way that we may choose the starting points, i.e. inside, outside or on the boundaries of the feasible region.