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Main research interests

My main research interest is convex 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.

Published and accepted papers

  1. Andreani, Roberto; Haeser, Gabriel, Schuverdt, María L. and Silva, Paulo J. S. A relaxed constant positive linear dependence constraint qualification and applications. To appear in Mathematical Programming, series A. DOI: 10.1007/s10107-011-0456-0.
  2. de André, T. A. and Silva, Paulo J. S. Exact penalties for variational inequalities with applications to nonlinear complementarity problems . Computational Optimization and Applications, v. 47, p. 401-429, 2010, DOI: 10.1007/s10589-008-9232-3.
  3. Eckstein, Jonathan and Silva, Paulo J. S. Proximal methods for nonlinear programming: double regularizations and inexact subproblems . Computational Optimization and Applications, v. 46, p. 279-304, 2010, DOI: 10.1007/s10589-009-9274-1.
  4. Silva, Paulo J. S. and Humes, Carlos. Rescaled Proximal Methods ofr Linearly Constrained Convex Problems. RAIRO Operations Research, 41(4), p. 367-380, 2007. Download original technical report
  5. Auslender, A.; Silva, Paulo J. S., Teboulle, M. Nonmonotone Projected Gradient Methods Based on Barrier and Euclidean Distances. Computational Optimization and Applications, 38(3), p. 305-327, 2007.
  6. Barrera, Junior; Cesar Jr., Roberto M.; Humes Jr., Carlos; Martins Jr., David C.; Patrao, Diogo FC; Silva, Paulo J. S. Silva and Brentani, Helena. A feature selection approach for identification of signature genes from SAGE data. BMC Bioinformatics 8:169, 2007.
  7. Dellamonica Jr., Domingos; Silva, Paulo J. S.; Humes Jr, Carlos; Hirata, Nina S. T. and Barrera, Junior. An Exact Algorithm for Optimal MAE Stack Filter Design. IEEE Transactions on Imaging Processing, v. 16, p. 453-462, 2007.
  8. Silva, Paulo J. S. and Eckstein, J. Double-Regularization Proximal Methods, with Complementarity Applications. Computational Optimization and Applications 33:2-3, p. 115-156, 2006. Download original technical report
  9. Folgueira, Maria A. A. K.; Carraro, Dirce M.; Bretani, Helena, Patrão, Diogo F. C. P.; Barbosa, Edson M. Mourão Netto, Mário; Caldeira, José; R. F., Soares, Fernando A.Oliveira, Célia T.; Reis, Luiz F. L.; Kaiano, Jane H. L.; Camargo, Luiz P.; Vêncio, Ricardo Z. N.; Snitcovsky, Igor M. L.; Makdissi, Fabiana B. A.; Góes, João C. G. S.; Silva, Paulo J. S.; Katayam Maria L. H.; Bretani, Maria M. Gene expression profile associated to response to doxorubicin based therapy in breast cancer. Clinical Cancer Research 11: 7434--7443, 2005.
  10. Silva, Paulo J. S.; Hashimoto, Ronaldo; Kim, Seungchan; Barrera, Junior; Brandão, Leônidas; Suh, Edward and Dougherty, Edward. Feature Selection Algorithms to Find Strong Genes. Pattern Recognition Letters 26:10 1444-1453, 2005.
  11. Humes, Carlos; Silva, Paulo J. S. Inexact Proximal Point Algorithms and Descent Methods in Optimization. Optimization and Engineering 6(2): 257-271, 2005. Download original techinical report
  12. Alfredo Goldman, Fabio Kon, Paulo J. S. Silva, and Joe Yoder. Being Extreme in the Classroom: Experiences Teaching XP. Journal of the Brazilian Computer Society, v. 10(2): 1-17, 2004. Download
  13. Broda, Sabine; Damas, Luis; Finger, Marcelo; Silva, Paulo J. S.. The Decidability of a Fragment of BBÍW-Logic. Theoretical Computer Science 3:373-408, 2004.
  14. Humes, Carlos; Silva, Paulo J. S. and Svaiter, Benar. Some Inexact Hybrid Proximal Augmented Lagrangian Algorithms. Numerical Algorithms 35 (2-4): 175-184, 2004. Download original technical report
  15. Burachick, R. S.; Scheimberg, S. and Silva, Paulo J. S. A Note on the Existence of Zeroes of Convexly Regularized Sums of Maximal Monotone Operators. Journal of Mathematical Analysis and Applications 280: 313-320, 2003. Download original technical report
  16. Silva, Paulo J. S.; Eckstein, Jonathan and Humes, Carlos. Rescaling and Stepsize Selection in Proximal Methods using Separable Generalized Distances. SIAM Journal on Optimization 12(1): 238-261, 2001. Download original technical report
  17. Silva, Paulo J. S.; Queiroz, Marcelo and Humes, Carlos. A note on "Stability of clearing open loop policies in manufacturing systems". Computational and Applied Mathematics. 19(3), 339-348, 2000. Download original technical report
  18. Humes, Carlos; Silva, Paulo J. S. Strict Convex Regularizations, Proximal Point and Augmented Lagrangians. RAIRO Operations Research 34(3) 283-303, 2000.

    You may want to download the original technical report, RT-MAC 99-06. Download However beware that the journal version has major revisions.

Submitted papers

  1. Eckstein, Jonathan and Silva, Paulo J.S. A Practical Relative Error Criterion for Augmented Lagrangians , 2010.
  2. Andreani, Roberto; Fukuda, Ellen H. and Silva, Paulo J. S. A Gauss-Newton approach for solving constrained optimization problems using differentiable exact penalties, 2010.
  3. Andreani, Roberto; Haeser, Gabriel; Schuverdt, María Laura and Silva, Paulo J. S. Two new weak constraint qualifications and applications, 2011.
  4. Fukuda, Ellen H.; Silva, Paulo J. S. and Fukushima, Masao. Differentiable exact penalty functions for nonlinear second-order cone programs, 2011.

In the radar

Nowadays I am working on extensions of the exactl penalty approach for second order cone constrains, applications of the constant rank constraint qualification, and inexact augmented Lagrangians methods. There should be pre-prints on some of these subjects in this page soon.