Publications

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Journal Articles

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

Published in arXiv, 2026

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 constraint. 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.

Recommended citation: C. Audet, A. Brilli, Y. Diouane, S. Le Digabel, E. J. Silva, and C. Tribes. (2026). "A penalty-interior point method combined with MADS for equality and inequality constrained optimization." arXiv: 2601.20811 [math.OC]. 1(1).
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Nonlinear Derivative-free Constrained Optimization with a Penalty-Interior Point Method and Direct Search

Published in arXiv, 2025

In this work, we propose the joint use of a mixed penalty-interior point method and direct search, for addressing nonlinearly 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. Using CUTEst test problems, numerical experiments demonstrate the robustness, efficiency, and overall effectiveness of the proposed method, when compared with state-of-the-art solvers.

Recommended citation: A. Brilli, A. L. Custódio, G. Liuzzi, and E. J. Silva. (2025). "Nonlinear Derivative-free Constrained Optimization with a Penalty-Interior Point Method and Direct Search." arXiv: 2407.21634 [math.OC]. 1(1).
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An Inexact Restoration Direct Multisearch Filter Approach to Multiobjective Constrained Derivative-free Optimization

Published in Optimization Methods and Software, 2024

Direct Multisearch (DMS) is a well-established class of methods for multiobjective derivative-free optimization, where constraints are addressed by an extreme barrier approach, only evaluating feasible points. In this work, we propose the replacement of this extreme barrier approach by a filter strategy, combined with an inexact feasibility restoration step, to address constraints in the DMS framework. The filter approach treats feasibility as an additional component of the objective function that needs to be minimized. The inexact restoration step attempts to generate new feasible points, contributing to prioritize this feasibility, a requirement for the good performance of any filter approach. Theoretical results are provided, analysing the different types of sequences of points generated by the new algorithm, and numerical experiments on a set of nonlinearly constrained biobjective problems are reported, stating the good algorithmic performance of the proposed approach.

Recommended citation: E. J. Silva and A. L. Custódio. (2025). "An Inexact Restoration Direct Multisearch Filter Approach to Multiobjective Constrained Derivative-free Optimization." Optimization Methods and Software, 40(2), pp. 406-432. doi: 10.1080/10556788.2024.2412646.
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Integral Global Optimality Conditions and an Algorithm for Multiobjective Problems

Published in Numerical Functional Analysis and Optimization, 2024

In this work, we propose integral global optimality conditions for multiobjective problems not necessarily differentiable. The integral characterization, already known for single objective problems, are extended to multiobjective problems by weighted sum and Chebyshev weighted scalarizations. Using this last scalarization, we propose an algorithm for obtaining an approximation of the weak Pareto front whose effectiveness is illustrated by solving a collection of multiobjective test problems.

Recommended citation: Everton J. Silva, Elizabeth W. Karas and Lucelina B. Santos. (2022). "Integral Global Optimality Conditions and an Algorithm for Multiobjective Problems." Numerical Functional Analysis and Optimization. 43:10, 1265-1288, DOI: 10.1080/01630563.2022.2098503.
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Conference Papers

Desenvolvimento de Projetos em Robótica Educacional A inserção da Expressão Gráfica no ensino

Published in Anais da X Conferência Latino-Americana de Objetos e Tecnologias de Aprendizagem (LACLO 2015), 2015

This paper describes the implementation of projects development in the classroom using educational robotics as tool. The project-based learning shows as a great pedagogical practice to re-enchant the classrooms, in addition to providing a development of the currently required intellectual abilities. The experiment conducted consisted of a simple challenge, which students should solve using a robot, to develop the robot were used the methodologies of brainstorm and morphological matrix. At the end it was concluded that the proposal was satisfactory to be able to play an interdisciplinary activity, where the contents were experienced with meaning and intellectual and social skills were worked instinctively.

Recommended citation: Amanda F. Procek, Everton J. Silva, Renata R. N. Corrêa, Rodrigo L. Nogueira, Adriana A. B. S. Luz, Anderson R. Góes, Heliza C. Góes. (2015). "Desenvolvimento de Projetos em Robótica Educacional A inserção da Expressão Gráfica no ensino." Anais da X Conferência Latino-Americana de Objetos e Tecnologias de Aprendizagem (LACLO 2015). 1(3).
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Everton Silva