A neural network approach to variational problems

• Main Author: Jackson, Monica Christine
• Format: Others
• Published: DigitalCommons@Robert W. Woodruff Library, Atlanta University Center 1994
• Subjects: Mathematics
• Online Access: http://digitalcommons.auctr.edu/dissertations/3394; http://digitalcommons.auctr.edu/cgi/viewcontent.cgi?article=4922&context=dissertations

We study processes governed by linear differential equations with initial value constrained to be on a manifold. The first part of our study deals with the minimization of a quadratic cost which we solve numerically using IMSL routines after appropriate reformulation. The second part of our work adds more restrictions on the initial states and the method is based on ideas borrowed from neural networks. The idea is based on minimizing an energy function following a flow that is constrained on the manifold of initial states. The flow once on the manifold, stays on the manifold. These ideas are employed to study boundary value problems for ordinary differential equations and integral equations. Numerical implementation has also been investigated.