On Duality Principles and Related Convex Dual Formulations Suitable for Local and Global Non-Convex Variational Optimization
Fabio Botelho · Preprints.org · 2023
This article develops duality principles, a related convex dual formulation and primal dual formulations suitable for the local and global optimization of non-convex primal formulations for a large class of models in physics and engineering. The results are based on standard tools of functional analysis, calculus of variations and duality theory. In particular, we develop applications to a Ginzburg-Landau type equation. Other applications include primal dual variational formulations for a Burger's type equation and a Navier-Stokes system. We emphasize the novelty here is that the first dual variational formulation developed is convex for a primal formulation which is originally non-convex. Finally, we also highlight the primal dual variational formulations presented have a large region of convexity around any of their critical points.