  This article develops dual variational formulations for a large class of
models in variational optimization. The results are established through basic
tools of functional analysis, convex analysis and duality theory. The main
duality principle is developed as an application to a Ginzburg-Landau type
system in superconductivity in the absence of a magnetic field. In the first
part final sections, we develop new general dual convex variational
formulations, more specifically, dual formulations with a large region of
convexity around the critical points which are suitable for the non-convex
optimization for a large class of models in physics and engineering. Finally,
in the last section we present some numerical results concerning the
generalized method of lines applied to a Ginzburg-Landau type equation.
