Main research interests
My main research interest are convex and nonlinear optimization and its extensions, like nonlinear complementarity problems or variational inequalities. On these subjects I study the proximal point method and algorithms based on penalties and duality, like multiplier methods and differentiable exact penalties.
I am also interested on applications of optimization and support vector machines to pattern recognition, with special interest on bioinformatics, like the analysis of gene expression data.
In the radar
Nowadays I am working on using DC programming to develop robust Support Vector Machines and on using a spectral proximal gradient method to solve problems in image processing. You can expect preprints on these subject here soon.
Preprints
1. A unified analysis of descent sequences in weakly convex optimization, including convergence rates for bundle methods

Atenas, Sagastizábal, Silva and Solodov. Optimization Online, 2021.

Papers
1. Robot Dance: A mathematical optimization platform for intervention against COVID-19 in a complex network

Nonato et al. EURO Journal on Computational Optimization, 2022.

2. Smart testing and critical care bed sharing for COVID-19 control

Silva et al. PLOS One, 2021.

3. A mixed quadratic programming model for a robust support vector machine

Raquel Serna-Diaz, Raimundo Santos Leite, Paulo J. S. Silva. Selecciones Matemáticas, 2021.

4. On scaled stopping criteria for a safeguarded augmented Lagrangian method with theoretical guarantees

Andreani, Haeser, Schuverdt, Secchin, Silva, Mathematical Programming Computation, 2021.

5. Optimized delay of the second COVID-19 vaccine dose reduces ICU admissions

Silva et al. Proceeding of the National Academy of Science (PNAS), 2021.

6. A discussion on electricity prices, or the two sides of the coin

Luna, Sagastizábal, Silva. Philosophiccal Transactions A, 2021.

7. Erratum to New Constraint Qualifications and Optimality Conditions for Second Order Cone Programs

Andreani et al. Set-Valued and Variational Analysis, 2021.

8. TopoMap: A 0-dimensional Homology Preserving Projection of High-Dimensional Data

Doraiswamy, H.; Tierny, J.; Silva, P. J. S.; Nonato, L. G.; Silva, C. IEEE Transactions on Visualization and Computer Graphics, 2020.

9. New sequential optimality conditions for mathematical programs with complementarity constraints and algorithmic consequences

Andreani, Haeser, Secchin, Silva, SIAM Journal on Optimization, 2019.

10. Accelerating block coordinate descent methods with identification strategies

Lopes, Santos, and Silva, Computational Optimization and Applications, 2019.

11. Convergence properties of a second order augmented Lagrangian method for mathematical programs with complementarity constraints

Andreani, Secchin, and Silva, SIAM Journal on Optimization, 2018.

12. Strict constraint qualifications and sequential optimality conditions for constrained optimization

Andreani, Martínez, Ramos, and Silva, Mathematics of Operations Research, 2018.

13. Second-order sequential optimality condition associated to the convergence of optimization algorithms

Andreani, Haeser, Ramos, and Silva, IMA Journal of Numerical Analisys, 2017.

14. On second-order optimality conditions in nonlinear optimization

Andreani, Behling, Haeser, Silva. Optimization Methods & Software, 2016.

15. A cone-continuity constraint qualification and algorithmic consequences

Andreani, Martinez, Ramos, Silva. SIAM Journal on Optimization, 2016.

16. Constant rank constraint qualifications - a geometric introduction

Andreani, Silva. Pesquisa Operacional, 2014.

17. A Newton’s method for the continuous quadratic knapsack problem

Cominetti, Mascarenhas, and Silva. Mathematical Programming Computations, 2016.

18. A practical relative error criterion for augmented Lagrangians

Eckstein and Silva. Mathematical Programming (series A), 2013.

19. A Gauss–Newton approach for solving constrained optimization problems using differentiable exact penalties

Andreani, Fukuda, and Silva. Journal of Optimization Theory and Applications, 2013.

20. Differentiable exact penalty functions for nonlinear second-order cone programs

Fukuda, Silva, and Fukushima. SIAM Journal on Optimization, 2012.

21. Transcriptional alterations related to neuropathology and clinical manifestation of Alzheimer’s disease

Silva et. al. PLOS ONE, 2012.

22. Two new weak constraint qualifications and applications

Andreani, Haeser, Schuverdt, and Silva. SIAM Journal on Optimization, 2012.

23. A relaxed constant positive linear dependence constraint qualification and applications

Andreani, Haeser, Schuverdt, and Silva. Mathematical Programming (series A), 2012.

24. Exact penalties for variational inequalities with applications to nonlinear complementarity problems

André and Silva. Computational Optimization and Applications, 2010.

25. Proximal methods for nonlinear programming - double regularization and inexact subproblems

Eckstein and Silva. Computational Optimization and Applications, 2010.

26. Nonmonotone projected gradient methods based on barrier and Euclidean distances

Auslender, Teboulle, and Silva. Computational Optimization and Applications, 2007.

27. Rescaled proximal methods for linearly constrained convex problems

Silva and Humes. RAIRO Operations Research, 2007.

28. A feature selection approach for identification of signature genes from SAGE data

Barrera et al, BMC Bioinformatics, 2007.

29. An Exact Algorithm for Optimal MAE Stack Filter Design

Dellamonica et al., IEEE Transactions of Image Processing, 2007.

30. Double-Regularization Proximal Methods, with Complementarity Applications

Silva and Eckstein, Computation Optimization and Applications, 2006.

31. Gene Expression Profile Associated with Response to Doxorubicin-Based Therapy in Breast Cancer

Folgueira et al. Clinical Cancer Research, 2005.

32. Feature selection algorithms to find strong genes

Silva et al. Pattern Recognition Letters, 2005.

33. Inexact Proximal Point Algorithms and Descent Methods in Optimization

Carlos Humes Jr. and Paulo J. S. Silva. Optimization and Engineering, 2005.

34. Being Extreme in the Classroom - Experiences Teaching XP

Alfred Goldman, Fabio Kon, Paulo J. S. Silva and Joseph W. Yoder. Journal of the Brazilian Computer Society, 2004.

35. The decidability of a fragment of BB′IW-logic

Sabine Broda, Luı́s Damas, Marcelo Finger, and Paulo J. S. Silva. Theoretical Computer Science, 2004.

36. Some inexact hybrid proximal augmented Lagrangian algorithms

Carlos HumesJr., Paulo J.S. Silva, Benar F. Svaiter. Numerical Algorithms, 2004.

37. A note on the existence of zeroes of convexly regularized sums of maximal monotone operators

Regina S. Burachik, Susana Scheimberg, and Paulo J. S. Silva. Journal of Mathematical Analysis and Applications, 2003.

38. Rescaling and Stepsize Selection in Proximal Methods Using Separable Generalized Distances

Paulo J. S. Silva, Jonathan Eckstein, and Carlos Humes Jr. SIAM Journal on Optimization, 2001.

39. A note on "stability of clearing open loop policies in manufacturing systems"

Paulo J. S. Silva, Marcelo Queiroz, Carlos Humes Jr. Computational And Applied Mathematics, 2000.

40. Strict convex regularizations, proximal points and augmented lagrangians

Carlos Humes Jr. and Paulo J. S. Silva. RAIRO Operations Research, 2000.