Luiz-Rafael Santos

Luiz-Rafael Santos

Professor of Applied Mathematics and Optimization

Universidade Federal de Santa Catarina

Biography

I am Professor of Applied Mathematics and Optimization at Departamento de Matemática of Federal University of Santa Catarina - UFSC, located in Blumenau, SC, Brazil. I am also a member of the Laboratory of Computational and Applied Mathematics — LABMAC, where open-source solvers and algorithms in applied mathematics are developed.

My research interests include analysis and implementation of convex and nonconvex optimization algorithms, algorithms for data science and machine learning, and numerical linear algebra.


Resumé (in English).

CV Lattes (in Portuguese).

Interests

  • Optimization
  • Machine Learning Algorithms
  • Operations Research
  • Numerical Linear Algebra

Education

  • PhD in Applied Mathematics, 2014

    Unicamp, Brazil

  • MSc in Applied Mathematics, 2008

    Unicamp, Brazil

  • BSc in Mathematics, 2004

    FURB, Brazil

Experience

 
 
 
 
 

Professor of Applied Mathematics and Optimization

Universidade Federal de Santa Catarina

Sep 2014 – Present Blumenau, SC, BR
 
 
 
 
 

FAPESP Visiting Researcher at IMECC

Universidade Estadual de Campinas

Ago 2023 – Jan 2024 Campinas, SP, BR
 
 
 
 
 

Visiting Assistant Professor of Management Sciences and Engineering

Stanford University

Jan 2023 – Jul 2023 Stanford, CA, US
 
 
 
 
 

PhD Candidate in Applied Mathematics

Universidade Estadual de Campinas

Mar 2009 – Jul 2014 Campinas, SP, Brasil

Publications

Papers on the pipeline

1. Behling, R., Bello-Cruz, Y., & Santos, L.-R. (2023). Applications of the circumcentered-reflection method on variational problems. In progress.
2. Chu, Y.-C., Santos, L.-R., & Udell, M. (2023). Randomized preconditioners for Interior Point Methods. In progress.
3. Villas-Bôas, F. R., Santos, L.-R., & Oliveira, A. R. L. (2023). An Interior Point Method with no centrality parameter. In progress.
4. Behling, R., Bello-Cruz, Y., Iusem, A., Liu, D., & Santos, L.-R. (2023, August 18). A finitely convergent circumcenter method for the Convex Feasibility Problem. http://arxiv.org/abs/2308.09849

Peer reviewed articles on academic journals

1. Arefidamghani, R., Behling, R., Iusem, A. N., & Santos, L.-R. (2023). A circumcentered-reflection method for finding common fixed points of firmly nonexpansive operators. Journal of Applied and Numerical Optimization, (to appear). http://arxiv.org/abs/2203.02410
2. Behling, R., Bello-Cruz, Y., Iusem, A. N., & Santos, L.-R. (2023). On the centralization of the circumcentered-reflection method. Mathematical Programming. https://doi.org/10.1007/s10107-023-01978-w
3. Behling, R., Bello-Cruz, Y., Iusem, A., Liu, D., & Santos, L.-R. (2023). A successive centralized circumcenter reflection method for the convex feasibility problem. Computational Optimization and Applications. https://doi.org/10.1007/s10589-023-00516-w
4. Behling, R., Bello-Cruz, Y., Lara-Urdaneta, H., Oviedo, H., & Santos, L.-R. (2023). Circumcentric directions of cones. Optimization Letters, 17, 1069–1081. https://doi.org/10.1007/s11590-022-01923-4
5. Arefidamghani, R., Behling, R., Bello-Cruz, Y., Iusem, A. N., & Santos, L.-R. (2021). The circumcentered-reflection method achieves better rates than alternating projections. Computational Optimization and Applications, 79(2), 507–530. https://doi.org/10.1007/s10589-021-00275-6
6. Behling, R., Bello-Cruz, Y., & Santos, L.-R. (2021). Infeasibility and error bound imply finite convergence of alternating projections. SIAM Journal on Optimization, 31(4), 2863–2892. https://doi.org/10.1137/20M1358669
7. Behling, R., Bello-Cruz, Y., & Santos, L.-R. (2021). On the Circumcentered-Reflection Method for the Convex Feasibility Problem. Numerical Algorithms, 86, 1475–1494. https://doi.org/10.1007/s11075-020-00941-6
8. Santos, L.-R., & Bassanezi, R. C. (2009). Sistemas P-fuzzy Unidimiensionais com Condição Ambiental. Biomatemática, 19(1), 11–24. http://www.ime.unicamp.br/~biomat/bio19_art2.pdf
9. Behling, R., Bello-Cruz, Y., & Santos, L.-R. (2020). The block-wise circumcentered–reflection method. Computational Optimization and Applications, 76(3), 675–699. https://doi.org/10.1007/s10589-019-00155-0
10. Bueno, L. F., Haeser, G., & Santos, L.-R. (2020). Towards an efficient augmented Lagrangian method for convex quadratic programming. Computational Optimization and Applications, 76(3), 767–800. https://doi.org/10.1007/s10589-019-00161-2
11. Behling, R., Bello-Cruz, Y., & Santos, L.-R. (2018). Circumcentering the Douglas–Rachford method. Numerical Algorithms, 78(3), 759–776. https://doi.org/10.1007/s11075-017-0399-5
12. Santos, L.-R., Villas-Bôas, F. R., Oliveira, A. R. L., & Perin, C. (2019). Optimized choice of parameters in interior-point methods for linear programming. Computational Optimization and Applications, 73(2), 535–574. https://doi.org/10.1007/s10589-019-00079-9
13. Siqueira, A. S., Silva, R. C. da, & Santos, L.-R. (2016). Perprof-py: A Python Package for Performance Profile of Mathematical Optimization Software. Journal of Open Research Software, 4(e12), 5. https://doi.org/10.5334/jors.81
14. Filippozzi, R., Gonçalves, D. S., & Santos, L.-R. (2023). First-order methods for the convex hull membership problem. European Journal of Operational Research, 306(1), 17–33. https://doi.org/10.1016/j.ejor.2022.08.040
15. Behling, R., Bello-Cruz, Y., & Santos, L.-R. (2018). On the linear convergence of the circumcentered-reflection method. Operations Research Letters, 46(2), 159–162. https://doi.org/10.1016/j.orl.2017.11.018
16. Araújo, G. H. M., Arefidamghani, R., Behling, R., Bello-Cruz, Y., Iusem, A., & Santos, L.-R. (2022). Circumcentering approximate reflections for solving the convex feasibility problem. Fixed Point Theory and Algorithms for Sciences and Engineering, 2022(1), 30. https://doi.org/10.1186/s13663-021-00711-6

Peer reviewed proceedings and book chapters

1. Filippozzi, R., Gonçalves, D. S., & Santos, L.-R. (2023). Accelerating the Spherical Triangle Algorithm for the Convex-Hull Membership Problem. 4. https://www.siam.org/Portals/0/Conferences/OP/OP23_ABSTRACTS.pdf
2. Villas-Bôas, F. R., Oliveira, A. R. L., Perin, C., & Santos, L.-R. (2012). Polynomial Inequality Systems in Neighborhoods of the Central Path. Proceedings of the 3rd IMA Conference on Numerical Linear Algebra and Optimisation, 26.
3. Santos, L.-R., Villas-Bôas, F. R., Oliveira, A. R. L., & Perin, C. (2011). On a Polynomial Merit Function for Interior Point Methods. Proceedings of the 19th Triennial Conference of the International Federation of Operational Research Societies, 121.
4. Ertel, P. C. R., & Santos, L.-R. (2021). Otimização e análise teórica das máquinas de vetores suporte aplicadas à classificação de dados. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 8. https://proceedings.sbmac.org.br/sbmac/article/view/135598
5. Silva, T. da, & Santos, L.-R. (2021). Métodos iterativos para solução de sistemas lineares: aceleração usando reflexões circuncentradas. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 8. https://proceedings.sbmac.emnuvens.com.br/sbmac/article/view/136002
6. Filippozzi, R., Gonçalves, D. S., & Santos, L.-R. (2022). First-order methods for the convex-hull membership problem and applications. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 9. https://proceedings.sbmac.emnuvens.com.br/sbmac/article/view/3910

Dissertations

1. Santos, L.-R. (2004). Reconhecimento de faces utilizando pré-processamento através da transformada log-radon [Trabalho de Conclusão de Curso (in portuguese), Universidade Regional de Blumenau]. https://bu.furb.br/consulta/portalConsulta/recuperaMfnCompleto.php?menu=rapida&CdMFN=271220
2. Santos, L.-R. (2008). Strategies for pests control: p-fuzzy systems and hybrid control [Master's thesis (in portuguese), IMECC/Unicamp]. https://doi.org/10.47749/T/UNICAMP.2008.434021
3. Santos, L.-R. (2014). Optimized choice of parameters in interior-point methods for linear programming [PhD's thesis (in portuguese), IMECC/Unicamp]. https://doi.org/10.47749/T/UNICAMP.2014.931062