Many derivative-free methods for constrained problems are not efficient for minimizing functions on “thin” domains. Other algorithms, like those based on Augmented Lagrangians, deal with thin constraints using penalty-like strategies. When the constraints are computationally inexpensive but...

In a recent paper, Birgin, Floudas and Martínez introduced an augmented Lagrangian method for global optimization. In their approach, augmented Lagrangian subproblems are solved using the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\alpha $$</EquationSource> </InlineEquation> <Emphasis Type="SmallCaps">BB method and convergence to global minimizers was obtained assuming feasibility of the...</emphasis></equationsource></inlineequation>