Work

Nonlinear derivative-free constrained optimization with a penalty-interior point method and direct search

Year: 2026

Type: article

Abstract: In this work, the joint use of a mixed penalty-interior point method and direct search is proposed, to address nonlinear constrained derivative-free optimization problems. A merit function is considered, wherein the set of nonlinear inequality constraints is divided into two groups: one treated with a logarithmic barrier approach, and another, along with the equality constraints, addressed using a penalization term. This strategy is adapted and incorporated into a direct search method, enabling the effective handling of general nonlinear constraints. Convergence to KKT-stationary points is established under continuous differentiability assumptions, without requiring any kind of convexity. Computational experiments on analytical problems and an engineering application demonstrate the robustness, efficiency, and overall effectiveness of the proposed method, when compared with state-of-the-art solvers.

Source: Numerical Algorithms

DOI: 10.1007/s11075-026-02360-5

Authors: Andrea Brilli, Ana L. Custódio, Giampaolo Liuzzi, Everton J. Silva

Institutions: Sapienza University of Rome, NOVAMath Center for Mathematics and Applications, Universidade Nova de Lisboa, National Research Council, Istituto di Analisi dei Sistemi ed Informatica Antonio Ruberti

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Polytechnique Montréal