# Bayesian optimization under mixed constraints with a slack-variable augmented Lagrangian

arXiv: https://arxiv.org/abs/1605.09466 · HTML: https://mlsanity.com/paper/1605.09466/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2016.

## Built on by (most cited first, 29 of 29)

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## Abstract (arXiv)

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.