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arXiv · 2601.20811

A penalty-interior point method combined with MADS for equality and inequality constrained optimization

Charles Audet·Andrea Brilli·Youssef Diouane·Sébastien Le Digabel·Everton J. Silva·Christophe Tribes
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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.

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Charles Audet, Andrea Brilli, Youssef Diouane, Sébastien Le Digabel, Everton J. Silva, Christophe Tribes. 2026-01-28. A penalty-interior point method combined with MADS for equality and inequality constrained optimization. https://arxiv.org/abs/2601.20811

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