A penalty-interior point method combined with MADS for equality and inequality constrained optimization
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908794338934784 |
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| author | Audet, Charles Brilli, Andrea Diouane, Youssef Digabel, Sébastien Le Silva, Everton J. Tribes, Christophe |
| author_facet | Audet, Charles Brilli, Andrea Diouane, Youssef Digabel, Sébastien Le Silva, Everton J. Tribes, Christophe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20811 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A penalty-interior point method combined with MADS for equality and inequality constrained optimization Audet, Charles Brilli, Andrea Diouane, Youssef Digabel, Sébastien Le Silva, Everton J. Tribes, Christophe Optimization and Control 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. |
| title | A penalty-interior point method combined with MADS for equality and inequality constrained optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2601.20811 |