These are post-peer-review, pre-copyedit versions of articles published in journals. The final authenticated versions are available through the cited publication.

Algorithmic Design

  1. E. J. Silva and A. L. Custódio, An inexact restoration direct multisearch filter approach to multiobjective constrained derivative-free optimization (2023; submitted) PDF
  2. A. Mohammadi and A. L. Custódio, A trust region approach for computing Pareto fronts in Multiobjective Optimization, Computational Optimization and Applications, 87 (2024) 149-179  PDF
  3. A. L. Custódio, E. H. M. Krulikovski, and M. Raydan, A hybrid direct search and projected simplex gradient method for convex constrained minimization, doi: 10.1080/10556788.2023.2263618 (2023; online published in Optimization Methods and Software) PDF
  4. A. L. Custódio, R. Garmanjani, and M. Raydan, Derivative-free separable quadratic modeling and cubic regularization for unconstrained optimization, 4OR, 22 (2024) 121-144 PDF
  5. S. Tavares, C. P. Brás, A. L. Custódio, V. Duarte, and P. Medeiros, Parallel strategies for Direct Multisearch, Numerical Algorithms, 92 (2023) 1757-1788 PDF
  6. R. Andreani, A. L. Custódio, and M. Raydan, Using first-order information in Direct Multisearch for multiobjective optimization, Optimization Methods and Software, 37 (2022) 2135 - 2156 PDF
  7. A. L. Custódio, Y. Diouane, R. Garmanjani, and E. Riccietti, Worst-case complexity bounds of directional direct-search methods for multiobjective derivative-free optimization, Journal of Optimization Theory and Applications, 188 (2021) 73 - 93 PDF
  8. C. P. Brás and A. L. Custódio, On the use of polynomial models in multiobjective directional direct search, Computational Optimization and Applications, 77 (2020) 897-918 PDF
  9. R. G. Begiato, A. L. Custódio, and M. A. Gomes-Ruggiero, A global hybrid derivative-free method for high-dimensional systems of nonlinear equations, Computational Optimization and Applications, 75 (2020), 93 - 112. PDF
  10. A. L. Custódio and J. F. A. Madeira, MultiGLODS: Global and Local Multiobjective Optimization using Direct Search, Journal of Global Optimization, 72 (2018), 323 - 345. PDF
  11. A. L. Custódio and J. F. A. Madeira, GLODS: Global and Local Optimization using Direct Search, Journal of Global Optimization, 62 (2015) 1 - 28. PDF
  12. L. N. Vicente and A. L. Custódio, Analysis of direct searches for discontinuous functions, Mathematical Programming, 133 (2012), 299 - 325. PDF
  13. A. L. Custódio, J. F. A. Madeira, A. I. F. Vaz and L. N. Vicente, Direct Multisearch for Multiobjective Optimization, SIAM Journal on Optimization, 21 (2011), 1109 - 1140 (there is an errata for the published version). PDF
  14. A. L. Custódio, H. Rocha, and L. N. Vicente, Incorporating Minimum Frobenius Norm Models in Direct Search, Computational Optimization and Applications 46 (2010), 265 - 278. PDF
  15. A. L. Custódio, J. E. Dennis Jr. and L. N. Vicente, Using Simplex Gradients of Nonsmooth Functions in Direct Search Methods, IMA Journal of Numerical Analysis 28 (2008), 770 - 784. PDF
  16. C. Audet, A. L. Custódio and J. E. Dennis Jr., Erratum: Mesh Adaptive Direct Search Algorithms for Constrained Optimization, SIAM Journal on Optimization, 18 (2008) 1501 - 1503. PDF
  17. A. L. Custódio and L. N. Vicente, Using Sampling and Simplex Derivatives in Pattern Search Methods, SIAM Journal on Optimization, 18 (2007) 537 - 555. (complete numerical resultsPDF
  18. A. L. Custódio and R. C. Oliveira, Re-designing distribution operations: A case study on integrating inventory management and vehicle routes design, International Journal of Logistics Research and Applications, 9 (2006) 169 - 187.


  1. A. L. Custódio, K. Scheinberg, and L. N. Vicente, Methodologies and software for derivative-free optimization, Chapter 37 of Advances and Trends in Optimization with Engineering Applications (2017), T. Terlaky, M. F. Anjos, and S. Ahmed (editors), MOS-SIAM Book Series on Optimization, SIAM, Philadelphia. PDF
  2. A. L. Custódio, M. Emmerich, and J. F. A. Madeira, Recent Developments in Derivative-free Multiobjective Optimization, Computational Technology Reviews, 5 (2012), B. H. V. Topping (editor), Saxe-Coburg Publications, 1 - 30. PDF

Engineering Applications

  1. A. L. Custódio, M. A. Fortes, A. M. Sajo-Castelli, Filling holes under non-linear constraints, Computational and Applied Mathematics, 42 (2023) Article number 72 PDF
  2. J. V. Morais, A. L. Custódio, G. M. Marques, Calibration of parameters in Dynamic Energy Budget models using Direct-Search methods, Journal of Mathematical Biology, 78 (2019) 1439 - 1458. PDF
  3. Sofia D. Karamintziou, Ana Luísa Custódio, Brigitte Piallat, Mircea Polosan, Stéphan Chabardès, Pantelis G. Stathis, George A. Tagaris, Damianos E. Sakas, Georgia E. Polychronaki, George L. Tsirogiannis, Olivier David and Konstantina S. Nikita, Algorithmic design of a noise-resistant and efficient closed-loop deep brain stimulation system: a computational approach, PLoS ONE, 12 (2017), e0171458, 1 – 26.
  4. N. D. Gouveia, A. L. Custódio, D. M. Faria and A. P. Ramos, Determinação de relações tensão-abertura de fenda de BRFA através de análise inversa, Proceedings of the 9º Congresso Nacional de Mecânica Experimental, Aveiro, Portugal, 2014. PDF
  5. J. B. Cardoso, P. G. Coelho, and A. L. Custódio, Parallel Direct Search in Structural Optimization, in P. Iványi, B.H.V. Topping, (Editors), Proceedings of the Second International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, Civil-Comp Press, Stirlingshire, UK, Paper 48, 2011PDF


  1. Aplicações de Derivadas Simplécticas em Métodos de Procura Directa, PhD. Thesis, New University of Lisbon, Lisbon, 2007, in Portuguese. PDF
  2. Um Sistema de Gestão Logística Integrando Gestão de Inventário e Construção de Rotas, Master Thesis, IST, Lisbon, 2001, in Portuguese. PDF

Last updated: 21-09-2023