Ernesto G. Birgin Professor Department of Computer Science Institute of Mathematics and Statistics University of São Paulo |

Graduate in Computer Science, University of Buenos Aires, 1995. PhD in Applied Mathematics, State University of Campinas, 1998. Full Professor at the University of São Paulo.

Research interests: Linear and non-linear programming, numerical optimization, numerical linear algebra for optimization, computational differentiation, operational research, combinatorial optimization.

Member of the Continuous Optimization group at the Institute of Mathematics and Statistics of the University of São Paulo (in Portuguese).

Teaching, advisoring and Seminars (in Portuguese)

Software

- TANGO Project: Trustable Algorithms for Nonlinear General Optimization
- PUMA: Pointwise Unconstrained Minimization Approach (Estimation of the optical constants and the thickness of thin films)
- PACKMOL: Packing Optimization for Molecular Dynamics Simulations
- PACKING: manufacturer's pallet loading problem and a large variety of packing problems solved by nonlinear programming
- Code related to some papers (Packing, Spectral Conjugate Gradient, Inexact Variable Metric Methods, Augmented Lagrangians Comparison)

Book

E. G. Birgin and J. M. Martínez,Audience: This book is aimed at engineers, physicists, chemists, and other practitioners interested in full access to comprehensive and well-documented software for large-scale optimization as well as up-to-date convergence theory and its practical consequences. It will also be of interest to graduate and advanced undergraduate students in mathematics, computer science, applied mathematics, optimization, and numerical analysis. |

Refereed publications

- E. G. Birgin, J. L. Gardenghi, J. M. Martínez, and S. A. Santos, "On the use of third-order models with fourth-order regularization for unconstrained optimization",
*submitted*. [Abstract] [pdf] - E. G. Birgin and R. D. Lobato, "Large-scale packing of ellipsoids",
*submitted*. [Abstract] [pdf] [code] - E. G. Birgin, N. Krejic, and J. M. Martínez, "Iteration and evaluation complexity on the minimization of functions whose computation is intrinsically inexact",
*submitted*. [Abstract] [pdf] - E. G. Birgin and J. M. Martínez, "On regularization and active-set methods with complexity for constrained optimization",
*submitted*. [Abstract] [pdf] - E. G. Birgin, G. Haeser, and A. Ramos, "Augmented Lagrangians with constrained subproblems and convergence to second-order stationary points",
*Computational Optimization and Applications*, to appear. [Abstract] [pdf] [DOI: 10.1007/s10589-017-9937-2] - E. G. Birgin, N. Krejic, and J. M. Martínez, "On the employment of Inexact Restoration for the minimization of functions whose evaluation is subject to errors",
*Mathematics of Computation*, to appear. [Abstract] [pdf] [DOI: 10.1090/mcom/3246] - E. G. Birgin, N. Krejic, and J. M. Martínez, "On the minimization of possibly discontinuous functions by means of pointwise approximations",
*Optimization Letters*11, pp. 1623-1637, 2017. [Abstract] [pdf] [DOI: 10.1007/s11590-016-1068-7] - E. G. Birgin, R. D. Lobato, and J. M. Martínez, "A nonlinear programming model with implicit variables for packing ellipsoids",
*Journal of Global Optimization*68, pp. 467-499, 2017. [Abstract] [pdf] [Code] [DOI: 10.1007/s10898-016-0483-8] - E. G. Birgin and J. M. Martínez, "The use of quadratic regularization with a cubic descent condition for unconstrained optimization",
*SIAM Journal on Optimization*27, pp. 1049-1074, 2017. [Abstract] [pdf] [Code] [DOI: 10.1137/16M110280X] - E. G. Birgin, J. L. Gardenghi, J. M. Martínez, S. A. Santos, and Ph. L. Toint, "Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models",
*Mathematical Programming*163, pp. 359-368, 2017. [Abstract] [pdf] [DOI: 10.1007/s10107-016-1065-8] - E. G. Birgin, L. F. Bueno, and J. M. Martínez, "Sequential equality-constrained optimization for nonlinear programming",
*Computational Optimization and Applications*65, pp. 699-721, 2016. [Abstract] [pdf] [DOI: 10.1007/s10589-016-9849-6] - E. G. Birgin, R. D. Lobato, and J. M. Martínez, "Constrained optimization with integer and continuous variables using inexact restoration and projected gradients",
*Bulletin of Computational Applied Mathematics*4, pp. 55-70, 2016. [Abstract] [pdf] - E. G. Birgin, R. D. Lobato, and J. M. Martínez, "Packing ellipsoids by nonlinear optimization",
*Journal of Global Optimization*65, pp. 709-743, 2016. [Abstract] [pdf] [code] [DOI: 10.1007/s10898-015-0395-z] - E. G. Birgin, J. L. Gardenghi, J. M. Martínez, S. A. Santos, and Ph. L. Toint, "Evaluation complexity for nonlinear constrained optimization using unscaled KKT conditions and high-order models",
*SIAM Journal on Optimization*26, pp. 951-967, 2016. [Abstract] [pdf] [DOI: 10.1137/15M1031631] - E. G. Birgin and J. M. Martínez, "On the application of an Augmented Lagrangian algorithm to some portfolio problems",
*EURO Journal on Computational Optimization*4, pp. 79-92, 2016. [Abstract] [pdf] [DOI: 10.1007/s13675-015-0052-9] - R. Andrade, E. G. Birgin, and R. Morabito, "Two-stage two-dimensional
guillotine cutting stock problems with usable leftovers",
*International Transactions in Operational Research*23, pp. 121-145, 2016. [Abstract] [pdf] [DOI: 10.1111/itor.12077] (See also the Technical Report MCDO110713 (extended version of the published article [pdf]) - M. Andretta, E. G. Birgin, and M. Raydan "An inner-outer nonlinear programming approach for constrained quadratic matrix model updating",
*Mechanical Systems and Signal Processing*66-67, pp. 78-88, 2016. [Abstract] [pdf] [DOI: 10.1016/j.ymssp.2015.05.002] (See also the Technical Report MCDO130814 (that includes additional details related to the numerical experiments [pdf]) - E. G. Birgin, J. E. Ferreira, and D. P. Ronconi, "List scheduling and beam search methods for an extended version of the flexible job shop scheduling problem",
*European Journal of Operational Research*247, pp. 421-440, 2015. [Abstract] [pdf] [Code] [DOI: 10.1016/j.ejor.2015.06.023]. - E. G. Birgin, J. M. Martínez, and L. F. Prudente, "Optimality
properties of an Augmented Lagrangian method on infeasible problems",
*Computational Optimization and Applications*60, pp. 609-631, 2015. [Abstract] [pdf] [DOI: 10.1007/s10589-014-9685-5] - E. G. Birgin, L. F. Bueno, and J. M. Martínez, "Assessing the reliability of general-purpose Inexact Restoration methods",
*Journal of Computational and Applied Mathematics*282, pp. 1-16, 2015. [Abstract] [pdf] [DOI: 10.1016/j.cam.2014.12.031] - C. S. Sakuraba, D. P. Ronconi, E. G. Birgin, and M. Yagiura, "Metaheuristics for large-scale instances of the linear ordering problem",
*Expert Systems with Applications*42, pp. 4432-4442, 2015. [Abstract] [pdf] [DOI: 10.1016/j.eswa.2015.01.053]. - R. Andrade, E. G. Birgin, R. Morabito, and D. P. Ronconi, "MIP models for two-dimensional non-guillotine cutting problems with usable leftovers",
*Journal of the Operational Research Society*65, pp. 1649-1663, 2014. [Abstract] [pdf] - E. G. Birgin, J. M. Martínez and M. Raydan, "Spectral Projected
Gradient methods: Review and Perspectives",
*Journal of Statistical Software*60(3), 2014. http://www.jstatsoft.org/v60/i03. [Abstract] [pdf] [Code] - E. G. Birgin, P. Feofiloff, C. G. Fernandes, E. L. de Melo,
M. T. I. Oshiro, and D. P. Ronconi, "A MILP model for an extended version
of the Flexible Job Shop Problem",
*Optimization Letters*8, pp. 1417-1431, 2014. [Abstract] [pdf] [Code] - E. G. Birgin, J. M. Martínez, and L. F. Prudente,
"Augmented Lagrangians with possible infeasibility and finite
termination for global nonlinear programming",
*Journal of Global Optimization*58, pp. 207-242, 2014. [Abstract] [pdf] [Code]. (See also the Technical Report MCDO250612 (extended version of the published article [pdf]) - E. G. Birgin, L. H. Bustamante, H. F. Callisaya, and J. M. Martínez,
"Packing circles within ellipses",
*International Transactions in Operational Research*20, pp. 365-389, 2013. [Abstract] [pdf] [Code] - E. G. Birgin, J. M. Martínez, L. Martínez, and G. B. Rocha,
"Sparse projected-gradient method as a linear-scaling low-memory
alternative to diagonalization in self-consistent field electronic
structure calculations",
*Journal of Chemical Theory and Computation*9, pp. 1043-1051, 2013. [Abstract] [pdf] - R. Andrade and E. G. Birgin, "Symmetry-breaking constraints for
packing identical orthogonal rectangles within polyhedra",
*Optimization Letters*7, pp. 375-405, 2013. [Abstract] [pdf] - M. Andretta and E. G. Birgin, "Deterministic and stochastic global
optimization techniques for planar covering with ellipses problems",
*European Journal of Operational Research*224, pp. 23-40, 2013. [Abstract] [pdf] [Code] - E. G. Birgin and J. M. Gentil, "Evaluating bound-constrained
minimization software",
*Computational Optimization and Applications*53, pp. 347-373, 2012. [Abstract] [pdf] [Code] - E. G. Birgin and D. P. Ronconi, "Heuristic methods for the single
machine scheduling problem with different ready times and a common due date",
*Engineering Optimization*44, pp. 1197-1208, 2012. [Abstract] [pdf] [Code] - E. G. Birgin, D. Fernandez and J. M. Martínez, "On the boundedness of
penalty parameters in an Augmented Lagrangian method with lower level
constraints",
*Optimization Methods and Software*27, pp. 1001-1024, 2012. [Abstract] [pdf] - E. G. Birgin and J. M. Martínez, "Augmented Lagrangian method with
nonmonotone penalty parameters for constrained optimization",
*Computational Optimization and Applications*51, pp. 941-965, 2012. [Abstract] [pdf] - E. G. Birgin, R. D. Lobato and R. Morabito, "Generating unconstrained
two-dimensional non-guillotine cutting patterns by a recursive partitioning
algorithm",
*Journal of the Operational Research Society*63, pp. 183-200, 2012. [Abstract] [pdf] [Code] - E. G. Birgin, L. F. Bueno, N. Krejic and J. M. Martínez, "Low
Order-Value approach for solving VaR-constrained optimization problems",
*Journal of Global Optimization*51, pp. 715-742, 2011. [Abstract] [pdf] [Code] - E. G. Birgin, E. V. Castelani, A. L. M. Martinez and J. M. Martínez,
"Outer Trust-Region method for Constrained Optimization",
*Journal of Optimization Theory and Applications*150, pp. 142-155, 2011. [Abstract] [pdf] [Code]. (See also the Technical Report MCDO251110 [pdf]) - E. G. Birgin and R. D. Lobato, "Orthogonal packing of identical
rectangles within isotropic convex regions",
*Computers & Industrial Engineering*59, pp. 595-602, 2010. [Abstract] [pdf] [Code] - E. G. Birgin, E. M. Gozzi, M.G.C. Resende and R.M.A. Silva,
"Continuous GRASP with a local active-set method for bound-constrained global
optimization",
*Journal of Global Optimization*48, pp. 289-319, 2010. [Abstract] [pdf] [Code] - E. G. Birgin, C. A. Floudas and J. M. Martínez, "Global minimization
using an Augmented Lagrangian method with variable lower-level constraints",
*Mathematical Programming*125, pp. 139-162, 2010. [Abstract] [pdf] [Code]. (See also the Technical Report MCDO121206 (including the formulations of the problems used in the numerical experiments) [pdf]) - W. F. Mascarenhas and E. G. Birgin, "Using sentinels to detect
intersections of convex and nonconvex polygons",
*Computational & Applied Mathematics*29, pp. 247-267, 2010. [Abstract] [pdf] - R. Andreani, E. G. Birgin, J. M. Martínez and M. L. Schuverdt,
"Second-order negative-curvature methods for box-constrained and general
constrained optimization",
*Computational Optimization and Applications*45, pp. 209-236, 2010. [Abstract] [pdf]. - E. G. Birgin, R. D. Lobato and R. Morabito, "An effective recursive
partitioning approach for the packing of identical rectangles in a rectangle",
*Journal of the Operational Research Society*61, pp. 306-320, 2010. [Abstract] [pdf] [ps] [Code] - E. G. Birgin and J. M. Gentil, "New and improved results for packing
identical unitary radius circles within triangles, rectangles and strips",
*Computers & Operations Research*37, pp. 1318-1327, 2010. [Abstract] [pdf] [Code] - M. Andretta, E. G. Birgin and J. M. Martínez, "Partial Spectral
Projected Gradient Method with Active-Set Strategy for Linearly Constrained
Optimization",
*Numerical Algorithms*53, pp. 23-52, 2010. [Abstract] [pdf] [Code]. (See also the Technical Report MCDO090309 (including tables with the full description of the numerical experiments) [pdf]) - L. Martínez, R. Andrade, E. G. Birgin and J. M. Martínez, "PACKMOL: A
package for building initial configurations for molecular dynamics
simulations",
*Journal of Computational Chemistry*30, pp. 2157-2164, 2009. [Abstract] [pdf] [Code] - R. Andrade, E. G. Birgin, I. Chambouleyron, J. M. Martínez and
S. D. Ventura, "Estimation of the thickness and the optical parameters of
several superimposed thin films using optimization",
*Applied Optics*47, pp. 5208-5220, 2008. [Abstract] [pdf] [ps]. - E. G. Birgin and J. M. Martínez, "Improving ultimate convergence of an
Augmented Lagrangian method",
*Optimization Methods and Software*23, pp. 177-195, 2008. [Abstract] [pdf] [ps] [Code] - E. G. Birgin and J. M. Martínez, "Structured minimal-memory inexact
quasi-Newton method and secant preconditioners for Augmented Lagrangian
Optimization",
*Computational Optimization and Applications*39, pp. 1-16, 2008. [Abstract] [pdf] [ps] [Code] - E. G. Birgin and F. N. C. Sobral, "Minimizing the object dimensions
in circle and sphere packing problems",
*Computers & Operations Research*35, pp. 2357-2375, 2008. [Abstract] [pdf] [ps] [Code] - R. Andreani, E. G. Birgin, J. M. Martínez and M. L. Schuverdt,
"Augmented Lagrangian methods under the Constant Positive Linear Dependence
constraint qualification",
*Mathematical Programming*111, pp. 5-32, 2008. [Abstract] [pdf] [ps] [Code] - R. Andreani, E. G. Birgin, J. M. Martínez and M. L. Schuverdt, "On
Augmented Lagrangian methods with general lower-level constraints",
*SIAM Journal on Optimization*18, pp. 1286-1309, 2008. [Abstract] [pdf] [ps] [Code]. (See also the Technical Report MCDO151005 (extended version of the published article) [pdf] [ps]) - E. G. Birgin, J. M. Martínez, W. F. Mascarenhas and D. P. Ronconi
"Method of Sentinels for Packing Items within Arbitrary Convex Regions",
*Journal of the Operational Research Society*57, pp. 735-746, 2006. [Abstract] [pdf] [ps]. (See also the Technical Report MCDO230505 (including complete proofs) [pdf] [ps]) - E. G. Birgin, J. M. Martínez, F. H. Nishihara and D. P. Ronconi,
"Orthogonal packing of rectangular items within arbitrary convex regions by
nonlinear optimization",
*Computers & Operations Research*33, pp. 3535-3548, 2006. [Abstract] [pdf] [ps] [Code] - E. G. Birgin and J. M. Martínez, "Local convergence of an
Inexact-Restoration method and numerical experiments",
*Journal of Optimization Theory and Applications*127, pp. 229-247, 2005. [Abstract] [pdf] [ps]. (See also the Technical Report MCDO290405 (extended version of the published article)[pdf] [ps]) - E. G. Birgin, R. Morabito and F. H. Nishihara "A note on an L-approach
for solving the manufacturer's pallet loading problem",
*Journal of the Operational Research Society*56, pp. 1448-1451, 2005. [Abstract] [pdf] [ps] [Code] - S. D. Ventura, E. G. Birgin, J. M. Martínez and I. Chambouleyron,
"Optimization techniques for the estimation of the thickness and the optical
parameters of thin films using reflectance data",
*Journal of Applied Physics*97, 043512, 2005. [Abstract] [pdf] [ps] [Code] (See the new JAP six-character citation identifiers (CIDs).) - M. Andretta, E. G. Birgin and J. M. Martínez, "Practical active-set
Euclidian trust-region method with spectral projected gradients for
bound-constrained minimization",
*Optimization*54, pp. 305-325, 2005. [Abstract] [pdf] [ps] [Code] - E. G. Birgin, R. Castillo and J. M. Martínez, "Numerical comparison of
Augmented Lagrangian algorithms for nonconvex problems",
*Computational Optimization and Applications*31, pp. 31-55, 2005. [Abstract] [pdf] [ps] [Code] - E. G. Birgin and M. Raydan, "Robust stopping criteria for Dykstra's
algorithm",
*SIAM Journal on Scientific Computing*26, pp. 1405-1414, 2005. [Abstract] [pdf] [ps] - R. Andreani, E. G. Birgin, J. M. Martínez and J. Yuan, "Spectral
projected gradient and variable metric methods for optimization with linear
inequalities",
*IMA Journal of Numerical Analysis*25, pp. 221-252, 2005. [Abstract] [pdf] [ps] [Code] - E. G. Birgin, J. M. Martínez and D. P. Ronconi, "Optimizing the
Packing of Cylinders into a Rectangular Container: A Nonlinear Approach",
*European Journal of Operational Research*160, pp. 19-33, 2005. [Abstract] [pdf] [ps] [Code] - E. G. Birgin, J. M. Martínez and M. Raydan, "Inexact Spectral
Projected Gradient Methods on Convex Sets",
*IMA Journal of Numerical Analysis*23, pp. 539-559, 2003. [Abstract] [pdf] [ps] [Code] - E. G. Birgin, I. Chambouleyron, J. M. Martínez and S. D. Ventura,
"Estimation of optical parameters of very thin films",
*Applied Numerical Mathematics*47, pp. 109-119, 2003. [Abstract] [pdf] [ps] - E. G. Birgin, N. Krejic and J. M. Martínez, "Globally convergent
inexact quasi-Newton methods for solving nonlinear systems",
*Numerical Algorithms*32, pp. 249-260, 2003. [Abstract] [pdf] [ps] - E. G. Birgin, I. Chambouleyron and J. M. Martínez, "Optimization
problems in the estimation or parameters of thin films and the elimination of
the influence of the substrate",
*Journal of Computational and Applied Mathematics*152, pp. 35-50, 2003. [Abstract] [pdf] [ps] - E. G. Birgin, N. Krejic and J. M. Martínez, "Solution of bounded
nonlinear systems of equations using homotopies with inexact restoration",
*International Journal of Computer Mathematics*80, pp. 211-222, 2003. [Abstract] [pdf] [ps] - E. G. Birgin, J. M. Martínez and D. P. Ronconi, "Minimization
subproblems and heuristics for an applied clustering problem",
*European Journal of Operational Research*146, pp. 19-34, 2003. [Abstract] [pdf] [ps] - I. Chambouleyron, S. D. Ventura, E. G. Birgin and J. M. Martínez,
"Optical constants and thickness determination of very thin amorphous
semiconductor films",
*Journal of Applied Physics*92, pp. 3093-3102, 2002. [Abstract] [pdf] [ps] - E. G. Birgin and J. M. Martínez, "Large-scale active-set
box-constrained optimization method with spectral projected gradients",
*Computational Optimization and Applications*23, pp. 101-125, 2002. [Abstract] [pdf] [ps] [Code] - E. G. Birgin, J. M. Martínez and M. Raydan, "Algorithm 813: SPG -
software for convex-constrained optimization",
*ACM Transactions on Mathematical Software*27, pp. 340-349, 2001. [Abstract] [pdf] [ps] [Code] - E. G. Birgin and J. M. Martínez, "A spectral conjugate gradient method
for unconstrained optimization",
*Applied Mathematics and Optimization*43, pp. 117-128, 2001. [Abstract] [pdf] [ps] [Code] - M. Mulato, I. Chambouleyron, E. G. Birgin and J. M. Martínez,
"Determination of thickness and optical constants of a-Si:H films from
transmittance data",
*Applied Physics Letters*77, pp. 2133-2135, 2000. [Abstract] [pdf] [ps] [Code] - E. G. Birgin, J. M. Martínez and M. Raydan, "Nonmonotone spectral
projected gradient methods on convex sets",
*SIAM Journal on Optimization*10, pp. 1196-1211, 2000. [Abstract] [pdf] [ps] [Code] - E. G. Birgin, R. Biloti, M. Tygel and L. T. Santos, "Restricted
optimization: a clue to a fast and accurate implementation of the Common
Reflection Surface method",
*Journal of Applied Geophysics*42, pp. 143-155, 1999. [Abstract] [pdf] [ps] - E. G. Birgin, I. Chambouleyron and J. M. Martínez, "Estimation of the optical constants and the thickness of
thin films using unconstrained optimization",
*Journal of Computational Physics*151, pp. 862-880, 1999. [Abstract] [pdf] [ps] [Code] - E. G. Birgin and Y. G. Evtushenko, "Automatic differentiation and
spectral projected gradient methods for optimal control problems",
*Optimization Methods and Software*10, pp. 125-146, 1998. [Abstract] [pdf] [ps]

Other publications

- E. G. Birgin, "Applications of nonlinear programming to packing problems", in
*Applications + Practical Conceptualization + Mathematics = fruitful Innovation, Proceedings of the Forum of Mathematics for Industry 2014*, R. S. Anderssen, P. Broadbridge, Y. Fukumoto, K. Kajiwara, T. Takagi, E. Verbitskiy, and M. Wakayama (Eds.), Springer Series Mathematics for Industry 11, pp. 31-39, 2016. [Abstract] [pdf] [DOI: 10.1007/978-4-431-55342-7_3] - D. P. Ronconi and E. G. Birgin, "Mixed-integer programming models for
flowshop scheduling problems minimizing the total earliness and tardiness", in
*Just-in-Time Systems*, R. Z. Ríos-Mercado and Y. A. Ríos-Solís (Eds.),*Springer Series on Optimization and its Applications*60, 2012, pp. 91-105. [Abstract] [pdf] [Code] - E. G. Birgin, J. M. Martínez and M. Raydan, "Spectral
Projected Gradient Methods", in
*Encyclopedia of Optimization*, C. A. Floudas and P. M. Pardalos eds., 2nd ed., Springer US, 2009, pp. 3652-3659. [pdf] [ps] - E. G. Birgin and M. Raydan, "Dykstra's algorithm and
robust stopping criteria", in
*Encyclopedia of Optimization*, C. A. Floudas and P. M. Pardalos eds., 2nd ed., Springer US, 2009, pp. 828-833. [pdf] [ps] - E. G. Birgin and J. M. Martínez, "Practical Augmented
Lagrangian Methods", in
*Encyclopedia of Optimization*, C. A. Floudas and P. M. Pardalos eds., 2nd ed., Springer US, 2009, pp. 3013-3023. [pdf] [ps] - E. G. Birgin and J. M. Martínez, "A box-constrained optimization
algorithm with negative curvature directions and spectral projected
gradients",
*Computing [Suppl]*15, pp. 49-60, 2001. [Abstract] [pdf] [ps] - E. G. Birgin and Y. G. Evtushenko, "Automatic differentiation
for optimal control problems", in
*Dynamics of Non-homogeneous System*, edited by Y. S. Popkov, Proceedings of ISA RAS, Institute of System Analysis of the Russian Academy of Science, Moscow, Vol. 2, pp. 53-62, 1999. [Abstract] [pdf] [ps]**Editorial material:** - E. G. Birgin, N. Krejic, J. M. Martínez, and M. Raydan, "Foreword special issue dedicated to selected surveys in Nonlinear Programming",
*Pesquisa Operacional*34, pp. 371-372, 2014. [pdf]. - E. G. Birgin, "Preface of the Special Issue on Nonlinear Programming
dedicated to the ALIO-INFORMS Joint International Meeting 2010",
*Computational and Applied Mathematics*30, pp. 1-3, 2011. [pdf] - E. G. Birgin, "Preface of the Special Issue dedicated to the VII
Brazilian Workshop on Continuous Optimization",
*Computational Optimization and Applications*46, pp. 189-191, 2010. [pdf]

**Refereed chapters of books:**

Contact

Department of Computer Science

Institute of Mathematics and Statistics

University of São Paulo

Rua do Matão, 1010 - Cidade Universitária

05508-090, São Paulo, SP - Brazil