An homotopy method for global optimization of continuous models

An original approach to global optimization of continuous models is introduced. It belongs to the class of homotopy continuation methods, but "only" requires non linear equation systems to be solved. Unconstrained and non-linearly constrained optimization problems are specified nearly the same way. They are solved by coupling a robust Newton formulation for under determinate systems and a heuristic estimating the global minimum value by means of the discrete Legendre-Fenchel biconjugate of the criterion. For the time being, the main drawback of the method is the too important number of function evaluations near by the global minimum. However, its success rate being very good on test problems, such as the global optimization of Lennard-Jones atomic clusters, it should be investigated further