Global minimization using an Augmented Lagrangian method with variable lower-level constraints

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the $${\varepsilon_{k}}$$ -global minimization of the Augmented Lagrangian with simple constraints, where $${\varepsilon_k \to \varepsilon}$$ . Global convergence to an $${\varepsilon}$$ -global minimizer of the original problem is proved. The subproblems are solved using the αBB method. Numerical experiments are presented.