S.Danipoul, Dr.S.Pradeep Gnanam
The Hopfield computational model is almost exclusively applied to the solution of combinatorial complex linear decision problems .The ability of networks of highly interconnected simple nonlinear analog processors (Neurons) to solve complicated optimization problems. A nonlinear neural framework called the Parameterized Hopfield Network is proposed, which is able to solve in a parallel distributed manner systems of nonlinear equations. The method is applied to the general nonlinear optimization problem. We demonstrate linear PHNs Cauchy and Newton dynamics are the two most important unconstrained optimization algorithms and nonlinear PHNs implementing the three most important optimization algorithms, namely the Augmented Lagrangian, Generalized Reduced Gradient and Successive Quadratic Programming methods. The study results in a dynamic view of the optimization problem and offers a straightforward model for the parallelization of the optimization computations, thus significantly extending the practical limits of problems that can be formulated as an optimization problem and which can gain from the introduction of nonlinearities in their structure (eg. pattern recognition, supervised learning, design of content-addressable memories).
Hopfield neural network, constrained optimization, Parameterized solution.