Report on Non Linear Optimization

[Manoel Fernando Tenorio]

This report is now available from Purdue University. There is a fee for 
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                    COMPUTATIONAL PROPERTIES OF
                   GENERALIZED HOPFIELD NETWORKS
                 APPLIED TO NONLINEAR OPTIMIZATION
 
                      Anthanasios G. Tsirukis
                               and
                       Gintaras V. Reklaitis
                   School of Chemical Engineering
 
                         Manoel F. Tenorio
                  School of Electrical Engineering
 
                    Technical Report TREE 89-69
		Parallel Distributed Structures Laboratory
                  School of Electrical Engineering
                         Purdue University
 
 
                              ABSTRACT
 
     A nonlinear neural framework, called the Generalized 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 optimization problem.  We demonstrate GHNs implementing the
three most important optimization algorithms, named 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).