<Para ID="Par1">Sometimes, the feasible set of an optimization problem that one aims to solve using a Nonlinear Programming algorithm is empty. In this case, two characteristics of the algorithm are desirable. On the one hand, the algorithm should converge to a minimizer of some infeasibility measure. On the...</para>

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>

A variant of the inexact augmented Lagrangian algorithm called SMALE (Dostál in Comput. Optim. Appl. 38:47–59, <CitationRef CitationID="CR10">2007</CitationRef>) for the solution of saddle point problems with a positive definite left upper block is studied. The algorithm SMALE-M presented here uses a fixed regularization parameter and...</citationref>