On a class of constrained functional minimization problems and their numerical solution

We investigate a class of functional minimization problems with constraints. By means of variational principles, optimal control theory, and numerical methods for nonlinear equations, numerical methods and the corresponding computer software are established to solve the problems. These tools can be used in fitting curves with arbitrary smoothness, different boundary conditions, and constraints. For special boundary conditions, analytical expressions of the curves are derived. Numerical examples are given to demonstrate the effectiveness of the algorithms by the means of curve fitting.