A bliss-type multiplier rule for constrained PDE variational problems
Abstract
A general multiplier rule is given for the Problem of Bolza for constrained optimization problems involving partial differential equations. These results are an extension of similar results by Bliss involving ordinary differential equations. Of special note is that these results will be used in later works by the authors to obtain new analytical techniques to solve general constrained problems involving PDEs for the Calculus of Variations and for Optimal Control Theory. They will also lead to new general, accurate and efficient numerical methods to solve these important problems where no such methods exist at this time. It is expected that these ideas will lead to analytical and numerical methods for applied problems in areas such as elasticity, optics, and mechanics.
