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}}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 e_k{\varepsilon_{k}} -global minimization of the Augmented Lagrangian with simple constraints, where e_k ? e{\varepsilon_k \to \varepsilon} . Global convergence to an e{\varepsilon} -global minimizer of the original problem is proved. The subproblems are solved using the αBB method. Numerical experiments are presented.