Ernesto G. Birgin

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: Nonlinear programming, optimization, operations research.

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

Book

E. G. Birgin and J. M. Martínez, Practical Augmented Lagrangian Methods for Constrained Optimization, Society for Industrial and Applied Mathematics, Philadelphia, 2014. [DOI: 10.1137/1.9781611973365]

This book focuses on Augmented Lagrangian techniques for solving practical constrained optimization problems. The authors rigorously delineate mathematical convergence theory based on sequential optimality conditions and novel constraint qualifications; orient the book to practitioners by giving priority to results that provide insight on the practical behavior of algorithms and by providing geometrical and algorithmic interpretations of every mathematical result; and fully describe a freely available computational package for constrained optimization and illustrate its usefulness with applications.

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.

Errata

Refereed publications

E. G. Birgin, A. Laurain, and D. R. Souza, Reconstruction of Voronoi diagrams: the case of inverse conductivity problems, submitted. [Abstract] [pdf] [code GitHub/local copy]
E. G. Birgin, J. A. Riveaux, and D. P. Ronconi, Energy-aware flexible job shop scheduling problem with nonlinear routes and position-based learning effect, submitted. [Abstract] [pdf] [code GitHub/local copy] (See also the Technical Report MCDO27062024 that corresponds to an extended version of the submitted article [pdf])
G. Q. Álvarez, E. G. Birgin, and J. M. Martínez, A first-order regularized algorithm with complexity properties for the unconstrained and the convexly constrained low order-value optimization problem, submitted. [Abstract] [pdf] [code GitHub/local copy]
E. G. Birgin, G. Haeser, N. Maculan, and L. Mallma Ramirez, On the global convergence of a general class of augmented Lagrangian methods, submitted. [Abstract] [pdf] [code]
K. A. G. Araujo, E. G. Birgin, and D. P. Ronconi, Local search and trajectory metaheuristics for the flexible job shop scheduling problem with nonlinear routes and position-based learning effect, submitted. [Abstract] [pdf] [code GitHub/local copy]
K. A. G. Araujo, E. G. Birgin, and D. P. Ronconi, Models, constructive heuristics, and benchmark instances for the flexible job shop scheduling problem with nonlinear routes and position-based learning effect, submitted. [Abstract] [pdf] [code GitHub/local copy]
E. G. Birgin and J. M. Martínez, On polynomial predictions for river surface elevations, Optimization and Engineering, to appear. [Abstract] [pdf] [DOI: 10.1007/s11081-024-09924-1] [Free access provided by SharedIt]
G. Q. Álvarez and E. G. Birgin, A first-order regularized approach to the order-value optimization problem, submitted. [Abstract] [pdf] [code GitHub/local copy]
E. G. Birgin, J. L. Gardenghi, D. S. Marcondes, and J. M. Martínez, Accelerated derivative-free spectral residual method for nonlinear systems of equations, submitted. [Abstract] [pdf] [code GitHub/local copy] [arXiv:2104.13447]
E. G. Birgin, A concise and friendly introduction to the analysis of algorithms for continuous nonlinear optimization, Coimbra Mathematical Texts, to appear. [Abstract] [pdf]
E. G. Birgin, G. Haeser, and J. M. Martínez, Safeguarded augmented Lagrangian algorithms with scaled stopping criterion for the subproblems, Computational Optimization and Applications, to appear. [Abstract] [pdf] [code] [DOI: 10.1007/s10589-024-00572-w] [Free access provided by SharedIt]
E. G. Birgin, A. Laurain, and D. R. Souza, Reconstruction of Voronoi diagrams in inverse potential problems, ESAIM: Control, Optimisation and Calculus of Variations 30, article number 85, 2024. [Abstract] [pdf] [code] [DOI: 10.1051/cocv/2024072]
E. G. Birgin, J. L. Gardenghi, and A. Laurain, Asymptotic bounds on the optimal radius when covering a set with minimum radius identical balls, Mathematics of Operations Research 49, pp. 1855-1889, 2024. [Abstract] [pdf] [code GitHub/local copy] [additional tables GitHub/local copy] [DOI: 10.1287/moor.2022.0104]
E. G. Birgin, M. R. Correa, V. A. González-López, J. M. Martínez, and D. S. Rodrigues, Randomly supported variation of deterministic models and its application to one-dimensional shallow water flows, Journal of Hydraulic Engineering 150, 04024026, 2024. [Abstract] [pdf] [code] [DOI: 10.1061/JHEND8.HYENG-13748]
E. G. Birgin and J. M. Martínez, A PDE-informed optimization algorithm for river flow predictions, Numerical Algorithms 96, pp. 289-304, 2024. [Abstract] [pdf] [code] [DOI: 10.1007/s11075-023-01647-1] [Free access provided by SharedIt]
E. G. Birgin and A. Laurain, Shape optimization for covering problems, Notices of the American Mathematical Society 70, pp. 1584-1591, 2023. [DOI: 10.1090/noti2799]
E. G. Birgin, A. Laurain, and T. C. Menezes, Sensitivity analysis and tailored design of minimization diagrams, Mathematics of Computation 92, pp. 2715-2768, 2023. [Abstract] [pdf] [code] [DOI: 10.1090/mcom/3839]
K. A. G. Araujo, E. G. Birgin, M. S. Kawamura, and D. P. Ronconi, Relax-and-fix heuristics applied to a real-world lot-sizing and scheduling problem in the personal care consumer goods industry, Operations Research Forum 4, article number 47, 2023. [Abstract] [pdf] [code GitHub/local copy] [DOI: 10.1007/s43069-023-00230-7] [Free access provided by SharedIt]
E. G. Birgin, O. C. Romão, and D. P. Ronconi, A forward-looking matheuristic approach for the multi-period two-dimensional non-guillotine cutting stock problem with usable leftovers, Expert Systems with Applications 223, article number 119866, 2023. [Abstract] [pdf] [code GitHub/local copy] [DOI: 10.1016/j.eswa.2023.119866]
E. G. Birgin, L. Fernandez, G. Haeser, and A. Laurain, Optimization of the first Dirichlet Laplacian eigenvalue with respect to a union of balls, The Journal of Geometric Analysis 33, article number 184, 2023. [Abstract] [pdf] [code] [DOI: 10.1007/s12220-023-01241-w] [Free access provided by SharedIt]
E. G. Birgin and J. M. Martínez, Secant acceleration of sequential residual methods for solving large-scale nonlinear systems of equations, SIAM Journal on Numerical Analysis 60, pp. 3145-3180, 2022. [Abstract] [pdf] [code] [DOI: 10.1137/20M1388024] [Free access to the published version]
V. A. Amaral, R. Andreani, E. G. Birgin, D. S. Marcondes, and J. M. Martínez, On complexity and convergence of high-order coordinate descent algorithms for smooth nonconvex box-constrained minimization, Journal of Global Optimization 84, pp. 527-561, 2022. [Abstract] [pdf] [code] [DOI: 10.1007/s10898-022-01168-6] [Free access provided by SharedIt]
E. G. Birgin, L. F. Bueno, and J. M. Martínez, On the complexity of solving feasibility problems with quadratically regularized models, Optimization Methods and Software 37, pp. 405-424, 2022. [Abstract] [pdf] [DOI: 10.1080/10556788.2020.1786564]
E. G. Birgin and J. M. Martínez, Block Coordinate Descent for smooth nonconvex constrained minimization, Computational Optimization and Applications 83, pp. 1-27, 2022. [Abstract] [pdf] [DOI: 10.1007/s10589-022-00389-5] [Free access provided by SharedIt]
E. G. Birgin, A. Laurain, R. Massambone, and A. G. Santana, A Shape-Newton approach to the problem of covering with identical balls, SIAM Journal on Scientific Computing 44, pp. A798-A824, 2022. [Abstract] [pdf] [code] [DOI: 10.1137/21M1426067] [Free access to the published version]
E. G. Birgin, N. Krejic, and J. M. Martínez, Economic inexact restoration for derivative-free expensive function minimization and applications, Journal of Computational and Applied Mathematics 410, 114193, 2022. [Abstract] [pdf] [DOI: 10.1016/j.cam.2022.114193]
E. G. Birgin and J. M. Martínez, Accelerated derivative-free nonlinear least-squares applied to the estimation of Manning coefficients, Computational Optimization and Applications 81, pp. 689-715, 2022. [Abstract] [pdf] [code] [DOI: 10.1007/s10589-021-00344-w] [Free access provided by SharedIt]
E. G. Birgin, J. L. Gardenghi, J. M. Martínez, and S. A. Santos, On the solution of linearly constrained optimization problems by means of barrier algorithms, TOP 29, pp. 417-441, 2021. [Abstract] [pdf] [code] [DOI: 10.1007/s11750-020-00559-w] [Free access provided by SharedIt]
E. G. Birgin, A. Laurain, R. Massambone, and A. G. Santana, A shape optimization approach to the problem of covering a two-dimensional region with minimum-radius identical balls, SIAM Journal on Scientific Computing 43, pp. A2047-A2078, 2021. [Abstract] [pdf] [code] [DOI: 10.1137/20M135950X] [Free access to the published version]
W. T. Lunardi, E. G. Birgin, D. P. Ronconi, and H. Voos, Metaheuristics for the Online Printing Shop Scheduling Problem, European Journal on Operational Research 293, pp. 419-441, 2021. [Abstract] [pdf] [code GitHub/local copy] [DOI: 10.1016/j.ejor.2020.12.021]
E. G. Birgin, J. M. Martínez, and A. Ramos, On constrained optimization with nonconvex regularization, Numerical Algorithms 86, pp. 1165-1188, 2021. [Abstract] [pdf] [DOI: 10.1007/s11075-020-00928-3] [Free access provided by SharedIt]
E. G. Birgin and J. M. Martínez, Complexity and performance of an Augmented Lagrangian algorithm, Optimization Methods and Software 35, pp. 885-920, 2020. [Abstract] [pdf] [code] [DOI: 10.1080/10556788.2020.1746962]
W. T. Lunardi, E. G. Birgin, P. Laborie, D. P. Ronconi, and H. Voos, Mixed Integer Linear Programming and Constraint Programming Models for the Online Printing Shop Scheduling Problem, Computers and Operations Research 123, Article number 105020, 2020. [Abstract] [pdf] [code GitHub/local copy] [DOI: 10.1016/j.cor.2020.105020]
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, Optimization Letters 14, pp. 815-838, 2020. [Abstract] [pdf] [code] [DOI: 10.1007/s11590-019-01395-z] [code] [Free access provided by SharedIt] (See also the Technical Report MCDO010418 "Third-order derivatives of the Moré, Garbow, and Hillstrom test set problems" [pdf])
E. G. Birgin, W. Gómez, G. Haeser, L. M. Mito, and D. S. Viana, An Augmented Lagrangian algorithm for nonlinear semidefinite programming applied to the covering problem, Computational and Applied Mathematics 39, article number 10, 2020. [Abstract] [pdf] [DOI: 10.1007/s40314-019-0991-5] [Free access provided by SharedIt]
E. G. Birgin, J. E. Ferreira, and D. P. Ronconi, A filtered beam search method for the m-machine permutation flowshop scheduling problem minimizing the earliness and the tardiness penalties and the waiting time of the jobs, Computers & Operations Research 114, article number 104824, 2020. [Abstract] [pdf] [code] [DOI: 10.1016/j.cor.2019.104824]
E. G. Birgin, O. C. Romão, and D. P. Ronconi, The multiperiod two-dimensional non-guillotine cutting stock problem with usable leftovers, International Transactions in Operational Research 27, pp. 1392-1418, 2020. [Abstract] [pdf] [DOI: 10.1111/itor.12648]
M. P. Martin, E. G. Birgin, R. D. Lobato, R. Morabito, and P. Munari, Models for the two-dimensional rectangular single large placement problem with guillotine cuts and constrained pattern, International Transactions in Operational Research 27, pp. 767-793, 2020. [Abstract] [pdf] [DOI: 10.1111/itor.12703]
E. G. Birgin, N. Krejic, and J. M. Martínez, Iteration and evaluation complexity for the minimization of functions whose computation is intrinsically inexact, Mathematics of Computations 89, pp. 253-278, 2020. [Abstract] [pdf] [DOI: 10.1090/mcom/3445]
E. G. Birgin and J. M. Martínez, A Newton-like method with mixed factorizations and cubic regularization for unconstrained minimization, Computational Optimization and Applications 73, pp. 707-753, 2019. [Abstract] [pdf] [code] [DOI: 10.1007/s10589-019-00089-7] [Free access provided by SharedIt]
E. G. Birgin and R. D. Lobato, A matheuristic approach with nonlinear subproblems for large-scale packing of ellipsoids, European Journal of Operational Research 272, 447-464, 2019. [Abstract] [pdf] [code] [DOI: 10.1016/j.ejor.2018.07.006]
E. G. Birgin and J. M. Martínez, On regularization and active-set methods with complexity for constrained optimization, SIAM Journal on Optimization 28, pp.1367-1395, 2018. [Abstract] [pdf] [DOI: 10.1137/17M1127107] [Free access to the published version]
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 87, pp. 1307-1326, 2018. [Abstract] [pdf] [DOI: 10.1090/mcom/3246]
E. G. Birgin, G. Haeser, and A. Ramos, Augmented Lagrangians with constrained subproblems and convergence to second-order stationary points, Computational Optimization and Applications 69, pp. 51-75, 2018. [Abstract] [pdf] [DOI: 10.1007/s10589-017-9937-2] [Free access provided by SharedIt]
E. G. Birgin, J. A. Cuminato, J. M. Martínez, and T. Pereira, CeMEAI: The Brazilian Center and Its Mathematics Research for Industry, Notices of the American Mathematical Society 64, pp. 450-454, 2017. [DOI: 10.1090/noti1513] [Free access to the published version]
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] [Free access provided by SharedIt]
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] [Free access provided by SharedIt]
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] [Free access to the published version]
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] [Free access provided by SharedIt]
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] [Free access provided by SharedIt]
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] [Free access provided by SharedIt]
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] [Free access to the published version]
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] [Free access provided by SharedIt]
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] [Free access provided by SharedIt]
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] [DOI: 10.1057/jors.2013.108] [Free access provided by SharedIt]
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] [DOI: 10.18637/jss.v060.i03]
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] [DOI: 10.1007/s11590-013-0669-7] [Free access provided by SharedIt]
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]. [DOI: 10.1007/s10898-013-0039-0] [Free access provided by SharedIt] (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] [DOI: 10.1111/itor.12006]
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] [DOI: 10.1021/ct3009683]
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] [DOI: 10.1007/s11590-011-0425-9] [Free access provided by SharedIt]
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] [DOI: 10.1016/j.ejor.2012.07.020]
E. G. Birgin and J. M. Gentil, Evaluating bound-constrained minimization software, Computational Optimization and Applications 53, pp. 347-373, 2012. [Abstract] [pdf] [code] [DOI: 10.1007/s10589-012-9466-y] [Free access provided by SharedIt]
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] [DOI: 10.1080/0305215X.2011.634409]
E. G. Birgin, D. Fernandez and J. M. Martínez, 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] [DOI: 10.1080/10556788.2011.556634]
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] [DOI: 10.1007/s10589-011-9396-0] [Free access provided by SharedIt]
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] [DOI: 10.1057/jors.2011.6] [Free access provided by SharedIt]
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] [DOI: 10.1007/s10898-011-9656-7] [Free access provided by SharedIt]
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]. [DOI: 10.1007/s10957-011-9815-5] [Free access provided by SharedIt] (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] [DOI: 10.1016/j.cie.2010.07.004]
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] [DOI: 10.1007/s10898-009-9494-z] [Free access provided by SharedIt]
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]. [DOI: 10.1007/s10107-009-0264-y] [Free access provided by SharedIt] (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] [DOI: 10.1590/S1807-03022010000200008]
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]. [DOI: 10.1007/s10589-009-9240-y] [Free access provided by SharedIt]
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] [DOI: 10.1016/j.cor.2009.09.017]
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] [DOI: 10.1016/j.cor.2009.09.017]
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]. [DOI: 10.1007/s11075-009-9289-9] (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] [DOI: 10.1002/jcc.21224]
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]. [DOI: 10.1364/AO.47.005208]
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] [DOI: 10.1080/10556780701577730]
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] [DOI: 10.1007/s10589-007-9050-z] [Free access provided by SharedIt]
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] [DOI: 10.1016/j.cor.2006.11.002]
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] [DOI: 10.1007/s10107-006-0077-1] [Free access provided by SharedIt]
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]. [DOI: 10.1137/060654797] [Free access to the published version] (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]. [DOI: 10.1057/palgrave.jors.2602067] (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] [DOI: 10.1016/j.cor.2005.03.031]
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]. [DOI: 10.1007/s10957-005-6537-6] [Free access provided by SharedIt] (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] [DOI: 10.1057/palgrave.jors.2601960]
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] [DOI: 10.1063/1.1849431]
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] [DOI: 10.1080/02331930500100270]
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] [DOI: 10.1007/s10589-005-1066-7] [Free access provided by SharedIt]
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] [DOI: 10.1137/03060062X] [Free access to the published version]
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] [DOI: 10.1093/imanum/drh020]
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] [DOI: 10.1016/j.ejor.2003.06.018]
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] [DOI: 10.1093/imanum/23.4.539]
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] [DOI: 10.1016/S0168-9274(03)00055-2]
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] [DOI: 10.1023/A:1024013824524] [Free access provided by SharedIt]
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] [DOI: 10.1016/S0377-0427(02)00695-7]
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] [DOI: 10.1080/00207160304672]
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] [DOI: 10.1016/S0377-2217(02)00208-4]
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] [DOI: 10.1063/1.1500785]
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] [DOI: 10.1023/A:1019928808826] [Free access provided by SharedIt]
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] [DOI: 10.1145/502800.502803]
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] [DOI: 10.1007/s00245-001-0003-0] [Free access provided by SharedIt]
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] [DOI: 10.1063/1.1314299]
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] [DOI: 10.1137/S1052623497330963] [Free access to the published version]
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] [DOI: 10.1016/S0926-9851(99)00035-X]
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] [DOI: 10.1006/jcph.1999.6224]
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] [DOI: 10.1080/10556789808805707]

Other publications

Refereed chapters of books:

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] [DOI: 10.1007/978-1-4614-1123-9_5]
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] [DOI: 10.1007/978-0-387-74759-0_629]
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] [DOI: 10.1007/978-0-387-74759-0_143]
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] [DOI: 10.1007/978-0-387-74759-0_517]
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] [DOI: 10.1007/978-3-7091-6217-0_5]
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, "Preface of the Special Issue dedicated to the XII Brazilian Workshop on Continuous Optimization", Computational Optimization and Applications 76, pp. 615-619, 2020. [pdf] [DOI: 10.1007/s10589-020-00203-0] [Free access provided by SharedIt]
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]. [DOI: 10.1590/0101-7438.2014.034.03.0371]
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] [DOI: 10.1590/S1807-03022011000100001]
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] [DOI: 10.1007/s10589-010-9325-7] [Free access provided by SharedIt]

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

egbirgin at ime.usp.br

+55.11.3091.6135 (phone)
+55.11.3091.6134 (phone/fax)
+55.11.3814.4135 (fax)