A penalty-interior point method combined with MADS for equality and inequality constrained optimization
Abstract
This work introduces MADS-PIP, an efficient framework that integrates a penalty-interior point strategy into the mesh adaptive direct search (MADS) algorithm for solving nonsmooth blackbox optimization problems with general inequality and equality constraints. Inequality constraints are partitioned into two subsets: one treated via a logarithmic barrier applied to an aggregated interior constraint violation, and the other handled through an exterior quadratic penalty. All equality constraints are treated by the exterior penalty. A merit function defines a sequence of unconstrained subproblems, which are solved approximately using MADS, while a carefully designed update rule drives the penalty-barrier parameter to zero. In the nonsmooth setting, we establish convergence results ensuring feasibility for general constraints as well as Clarke stationarity for inequality-constrained problems. Computational experiments on both analytical test sets and challenging blackbox problems demonstrate that the proposed MADS-PIP algorithm is competitive with, and often outperforms, MADS with the progressive barrier strategy, particularly in the presence of equality constraints.
Cite
@article{arxiv.2601.20811,
title = {A penalty-interior point method combined with MADS for equality and inequality constrained optimization},
author = {Charles Audet and Andrea Brilli and Youssef Diouane and Sébastien Le Digabel and Everton J. Silva and Christophe Tribes},
journal= {arXiv preprint arXiv:2601.20811},
year = {2026}
}