A preliminary report on the utilization of Galerkin-PSO method for solving interpolation-like problem

The interpolation-like problem discussed in this paper is to search an optimal curve minimizing a functional cost and at the same time interpolating several given points. Instead of solving the optimization problem with constrain directly, we transform the problem into a pure optimization problem, without constrain. After that, the Galerkin Method is used to make the problem finite dimensional one. The problem becomes finding a minimal point and value of a finite dimensional function. The Particle Swarm Optimization (PSO) algorithm is used to minimize this function.