  An augmented Lagrangian (AL) can convert a constrained optimization problem
into a sequence of simpler (e.g., unconstrained) problems, which are then
usually solved with local solvers. Recently, surrogate-based Bayesian
optimization (BO) sub-solvers have been successfully deployed in the AL
framework for a more global search in the presence of inequality constraints;
however, a drawback was that expected improvement (EI) evaluations relied on
Monte Carlo. Here we introduce an alternative slack variable AL, and show that
in this formulation the EI may be evaluated with library routines. The slack
variables furthermore facilitate equality as well as inequality constraints,
and mixtures thereof. We show how our new slack "ALBO" compares favorably to
the original. Its superiority over conventional alternatives is reinforced on
several mixed constraint examples.
