Everton Silva

Everton Silva

he/his/him

Ph.D. in Mathematics | Optimization

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A list of all the posts and pages found on the site. For you robots out there, there is an XML version available for digesting as well.

Pages

Posts

Future Blog Post

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Blog Post number 4

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Blog Post number 2

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Blog Post number 1

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portfolio

Optimality conditions for multiobjective problems

A study explored existence of solutions and Fritz–John and Karush–Kuhn–Tucker optimality conditions for nonlinear programming via Gordan’s alternative. It extends these results to multiobjective problems and examines invexity and KT-invexity, showing KKT conditions are necessary and sufficient in the broadest problem class.

Constraint qualification conditions for nonlinear programming problems

A continuation of prior research on Karush–Kuhn–Tucker conditions under key constraint qualifications (LICQ, Mangasarian–Fromovitz, Abadie, Guignard), examining their interrelations and impact on Lagrange multipliers. Using Motzkin’s Alternative Theorem and linear-programming duality, it aims to explore additional qualifications and extend findings to multiobjective optimization.

publications

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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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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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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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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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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talks

teaching

Module of Multiobjective Linear Optimization of the Linear Optimization

Course part of the MSc. Program in Analysis and Engineering of Big Data, NOVA University of Lisbon, Department of Mathmatics, 2022

Role: Lecturer (master’s-level module – 8h) Description: Invited by Professor Jorge Orestes Cerdeira (retired Full Professor, Department of Mathematics, NOVA School of Science and Technology) to design and deliver a dedicated module on Linear Multiobjective Optimization as part of the existing Linear Optimization syllabus. Conceived and produced comprehensive teaching materials, including well-structured slide decks, problem sets, and self-assessment exercises. Employed an interactive, student-centered pedagogy that balanced rigorous theoretical exposition with hands-on computational practice. Designed a project in which students developed algorithms to solve real-world problems, such as diet planning and cost optimization, fostering applied understanding of complex mathematical concepts. This approach promoted active learning, independent thinking, and adaptability to diverse student learning styles.

Matemática - Licenciatura em Gestão da Distribuição e Logistica

Undergraduate course, Polytechnic Institute of Setúbal, Department of Economics and Management, 2025

Mathematics — Bachelor’s in Distribution and Logistics Management (60h) Role: Lecturer (theoretical and practical classes). Description: Designed and delivered problem-solving classes focused on integral calculus, linear algebra and formulation/solution of linear programming problems. Emphasized student-centered learning through active in-class problem solving and collaborative exercises. Adopted a blended teaching approach—combining traditional lectures with interactive activities and contemporary digital resources—to foster critical thinking and equip students with practical tools for academic and professional challenges.

Introdução à Matemática - CTeSP

Undergraduate course, Polytechnic Institute of Setúbal, Department of Economics and Management, 2025

Introduction to Mathematics — Higher Technical Course in Logistics (Professional – 50h) Role: Lecturer and Course Coordinator (theoretical and practical classes). Description: Description: Provided a basic grounding in mathematics and descriptive statistics to prepare students for management practice. The course emphasized logical reasoning in management literature, practical analytical skills for decision-making, and the ability to interpret quantitative information in professional contexts.

Matemática Aplicada - Licenciatura em Marketing

Undergraduate course, Polytechnic Institute of Setúbal, Department of Economics and Management, 2025

Applied Mathematics — Bachelor’s in Marketing (45h) Role: Lecturer (theoretical and practical classes). Description: Delivered a foundational mathematics course for first-year Marketing students, emphasizing logical and analytical reasoning. The syllabus covered key topics in linear algebra and differential calculus essential for mathematical modelling, data analysis and problem-solving in economic and business contexts. Teaching combined structured lectures with practical sessions to develop students’ ability to apply mathematical tools to real-world marketing problems.