Computational methods of optimization

• Grant number: 06/53768-0
• Support type: Research Projects - Thematic Grants
• Duration: October 01, 2006 - September 30, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: José Mário Martinez Perez
• Grantee: José Mário Martinez Perez
• Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Co-Principal Investigators: Ana Friedlander de Martinez Perez
• Associated scholarship(s): 11/12203-8 - Broyden's methods to the feasibility problem and its relationship with inexact restoration methods, BP.PD; 11/03911-9 - Third order optimization methods, BP.MS; 09/00576-4 - Dynamic control of infeasibility for inequality constrained optimization, BP.DD; + associated scholarships 09/04785-7 - Automatic differentiation of Hessian matrices, BP.MS; 09/08027-0 - Global optimization applied to the tomography of quantum states, BP.DR; 09/00865-6 - Convergence, optimality conditions and properties on algorithms for non-linear programming problems, BP.DR; 07/08359-7 - Large scale problems in PDE-constrained optimization, BP.PD; 08/03590-5 - Hybrid metaheuristics for portfolio optimization, BP.IC; 08/04519-2 - Software for large-scale linearly constrained minimization problems, BP.PD; 07/06663-0 - Order value optimization applied to inverse Nash-Equilibrium, BP.DR - associated scholarships

Abstract

Research in the area of this project has been conducted in the Department of Applied Mathematics of the University of Campinas, under the direction of the coordinator, in the last 27 years. The group's interest area is optimization, undertaking research along its three main lines: Theory of problems and methods, practical implementation of algorithms and applications. We intend to build upon our previous work, in all its aspects, and, in particular, to continue the thematic project 2001/04597-4, which had the same title and coordinator. The team of the current proposal participates in the PRONEX on optimization. (AU)

Scientific publications

(45)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

KREJIC, NATASA; MARTINEZ, J. M. INEXACT RESTORATION APPROACH FOR MINIMIZATION WITH INEXACT EVALUATION OF THE OBJECTIVE FUNCTION. Mathematics of Computation, v. 85, n. 300, p. 1775-1791, JUL 2016. Web of Science Citations: 6.

ANDREANI, R.; JUDICE, J. J.; MARTINEZ, J. M.; MARTINI, T. Feasibility problems with complementarity constraints. European Journal of Operational Research, v. 249, n. 1, p. 41-54, FEB 16 2016. Web of Science Citations: 3.

CARVALHO, ESDRAS P.; MARTINEZ, JULIAN; MARTINEZ, J. M.; PISNITCHENKO, FEODOR. On optimization strategies for parameter estimation in models governed by partial differential equations. MATHEMATICS AND COMPUTERS IN SIMULATION, v. 114, p. 14-24, AUG 2015. Web of Science Citations: 3.

WASHINGTON ALVES DE OLIVEIRA; ANTONIO CARLOS MORETTI; EDNEI FELIX REIS. MULTI-VEHICLE COVERING TOUR PROBLEM: BUILDING ROUTES FOR URBAN PATROLLING. Pesquisa Operacional, v. 35, n. 3, p. 617-644, Dez. 2015.

GOMES, FRANCISCO A. M.; SENNE, THADEU A. An algorithm for the topology optimization of geometrically nonlinear structures. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, v. 99, n. 6, p. 391-409, AUG 10 2014. Web of Science Citations: 8.

ANDREANI, R.; MARTINEZ, J. M.; SANTOS, L. T.; SVAITER, B. F. On the behaviour of constrained optimization methods when Lagrange multipliers do not exist. OPTIMIZATION METHODS & SOFTWARE, v. 29, n. 3, p. 646-657, MAY 4 2014. Web of Science Citations: 7.

BIRGIN, E. G.; MARTINEZ, J. M.; PRUDENTE, L. F. Augmented Lagrangians with possible infeasibility and finite termination for global nonlinear programming. Journal of Global Optimization, v. 58, n. 2, p. 207-242, FEB 2014. Web of Science Citations: 10.

GOWER, ROBERT MANSEL; MELLO, MARGARIDA PINHEIRO. Computing the Sparsity Pattern of Hessians Using Automatic Differentiation. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, v. 40, n. 2 FEB 2014. Web of Science Citations: 3.

MARTINEZ, J. M.; SOBRAL, F. N. C. Constrained derivative-free optimization on thin domains. Journal of Global Optimization, v. 56, n. 3, SI, p. 1217-1232, JUL 2013. Web of Science Citations: 12.

BIRGIN, ERNESTO G.; BUSTAMANTE, LUIS HENRIQUE; CALLISAYA, HECTOR FLORES; MARTINEZ, JOSE MARIO. Packing circles within ellipses. International Transactions in Operational Research, v. 20, n. 3, p. 365-389, MAY 2013. Web of Science Citations: 7.

ANDRADE, R.; BIRGIN, E. G. Symmetry-breaking constraints for packing identical rectangles within polyhedra. Optimization Letters, v. 7, n. 2, p. 375-405, FEB 2013. Web of Science Citations: 4.

ANDREANI, ROBERTO; FUKUDA, ELLEN H.; SILVA, PAULO J. S. A Gauss-Newton Approach for Solving Constrained Optimization Problems Using Differentiable Exact Penalties. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, v. 156, n. 2, p. 417-449, FEB 2013. Web of Science Citations: 5.

BIRGIN, ERNESTO G.; MARTINEZ, J. M.; MARTINEZ, LEANDRO; ROCHA, GERD B. 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, v. 9, n. 2, p. 1043-1051, FEB 2013. Web of Science Citations: 10.

ANDRETTA, M.; BIRGIN, E. G. Deterministic and stochastic global optimization techniques for planar covering with ellipses problems. European Journal of Operational Research, v. 224, n. 1, p. 23-40, JAN 1 2013. Web of Science Citations: 0.

BUENO, L. F.; FRIEDLANDER, A.; MARTINEZ, J. M.; SOBRAL, F. N. C. INEXACT RESTORATION METHOD FOR DERIVATIVE-FREE OPTIMIZATION WITH SMOOTH CONSTRAINTS. SIAM JOURNAL ON OPTIMIZATION, v. 23, n. 2, p. 1189-1213, 2013. Web of Science Citations: 21.

ANDREANI, ROBERTO; HAESER, GABRIEL; LAURA SCHUVERDT, MARIA; SILVA, PAULO J. S. A relaxed constant positive linear dependence constraint qualification and applications. MATHEMATICAL PROGRAMMING, v. 135, n. 1-2, p. 255-273, OCT 2012. Web of Science Citations: 61.

BIRGIN, ERNESTO G.; GENTIL, JAN M. Evaluating bound-constrained minimization software. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 53, n. 2, SI, p. 347-373, OCT 2012. Web of Science Citations: 14.

MARTINEZ, JOSE MARIO; PRUDENTE, LEANDRO DA FONSECA. Handling infeasibility in a large-scale nonlinear optimization algorithm. NUMERICAL ALGORITHMS, v. 60, n. 2, SI, p. 263-277, JUN 2012. Web of Science Citations: 9.

CARVALHO, ESDRAS P.; PISNITCHENKO, FEODOR; MEZZOMO, NATALIA; FERREIRA, SANDRA R. S.; MARTINEZ, J. M.; MARTINEZ, JULIAN. Low Order-Value Multiple Fitting for supercritical fluid extraction models. Computers & Chemical Engineering, v. 40, p. 148-156, MAY 11 2012. Web of Science Citations: 4.

BIRGIN, ERNESTO G.; MARTINEZ, J. M. Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 51, n. 3, p. 941-965, APR 2012. Web of Science Citations: 33.

ANDREANI, ROBERTO; HAESER, GABRIEL; LAURA SCHUVERDT, MARIA; SILVA, PAULO J. S. TWO NEW WEAK CONSTRAINT QUALIFICATIONS AND APPLICATIONS. SIAM JOURNAL ON OPTIMIZATION, v. 22, n. 3, p. 1109-1135, 2012. Web of Science Citations: 43.

BIRGIN, ERNESTO G.; RONCONI, DEBORA P. Heuristic methods for the single machine scheduling problem with different ready times and a common due date. ENGINEERING OPTIMIZATION, v. 44, n. 10, p. 1197-1208, 2012. Web of Science Citations: 7.

BIRGIN, ERNESTO G.; FERNANDEZ, DAMIAN; MARTINEZ, J. M. The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems. OPTIMIZATION METHODS & SOFTWARE, v. 27, n. 6, p. 1001-1024, 2012. Web of Science Citations: 27.

GOWER, R. M.; MELLO, M. P. A new framework for the computation of Hessians. OPTIMIZATION METHODS & SOFTWARE, v. 27, n. 2, SI, p. 251-273, 2012. Web of Science Citations: 8.

BIRGIN, E. G.; BUENO, L. F.; KREJIC, N.; MARTINEZ, J. M. Low order-value approach for solving VaR-constrained optimization problems. Journal of Global Optimization, v. 51, n. 4, p. 715-742, DEC 2011. Web of Science Citations: 9.

FRANCISCO, JULIANO B.; MARTINEZ, J. M.; MARTINEZ, LEANDRO; PISNITCHENKO, FEODOR. Inexact restoration method for minimization problems arising in electronic structure calculations. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 50, n. 3, p. 555-590, DEC 2011. Web of Science Citations: 9.

BIRGIN, ERNESTO G.; CASTELANI, EMERSON V.; MARTINEZ, ANDRE L. M.; MARTINEZ, J. M. Outer Trust-Region Method for Constrained Optimization. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, v. 150, n. 1, p. 142-155, JUL 2011. Web of Science Citations: 8.

ANDREANI, R.; SANTOS, S. A.; SHIRABAYASHI, W. V. I. Newton-type interior-point methods for solving generalized complementarity problems in polyhedral cones. OPTIMIZATION, v. 60, n. 8-9, SI, p. 1171-1191, 2011. Web of Science Citations: 0.

ANDREANI, ROBERTO; HAESER, GABRIEL; MARTINEZ, J. M. On sequential optimality conditions for smooth constrained optimization. OPTIMIZATION, v. 60, n. 5, SI, p. 627-641, 2011. Web of Science Citations: 50.

DINIZ-EHRHARDT, M. A.; MARTINEZ, J. M.; PEDROSO, L. G. Derivative-free methods for nonlinear programming with general lower-level constraints. COMPUTATIONAL & APPLIED MATHEMATICS, v. 30, n. 1, p. 19-52, 2011. Web of Science Citations: 23.

FRIEDLANDER, ANA; GOMES, FRANCISCO A. M. Solution of a truss topology bilevel programming problem by means of an inexact restoration method. COMPUTATIONAL & APPLIED MATHEMATICS, v. 30, n. 1, p. 109-125, 2011. Web of Science Citations: 4.

GOMES, FRANCISCO A. M.; SENNE, THADEU A. An SLP algorithm and its application to topology optimization. COMPUTATIONAL & APPLIED MATHEMATICS, v. 30, n. 1, p. 53-89, 2011. Web of Science Citations: 10.

GOMES-RUGGIERO, MARCIA A.; SACHINE, MAEL; SANTOS, SANDRA A. Solving the dual subproblem of the Method of Moving Asymptotes using a trust-region scheme. COMPUTATIONAL & APPLIED MATHEMATICS, v. 30, n. 1, p. 151-170, 2011. Web of Science Citations: 2.

BIRGIN, ERNESTO G.; LOBATO, RAFAEL D. Orthogonal packing of identical rectangles within isotropic convex regions. COMPUTERS & INDUSTRIAL ENGINEERING, v. 59, n. 4, p. 595-602, NOV 2010. Web of Science Citations: 17.

BIRGIN, E. G.; FLOUDAS, C. A.; MARTINEZ, J. M. Global minimization using an Augmented Lagrangian method with variable lower-level constraints. MATHEMATICAL PROGRAMMING, v. 125, n. 1, p. 139-162, SEP 2010. Web of Science Citations: 75.

BIRGIN, ERNESTO G.; GENTIL, JAN M. New and improved results for packing identical unitary radius circles within triangles, rectangles and strips. Computers & Operations Research, v. 37, n. 7, p. 1318-1327, JUL 2010. Web of Science Citations: 37.

BIRGIN, E. G.; LOBATO, R. D.; MORABITO, R. An effective recursive partitioning approach for the packing of identical rectangles in a rectangle. Journal of the Operational Research Society, v. 61, n. 2, p. 306-320, FEB 2010. Web of Science Citations: 27.

ANDRETTA, MARINA; BIRGIN, ERNESTO G.; MARTINEZ, J. M. Partial spectral projected gradient method with active-set strategy for linearly constrained optimization. NUMERICAL ALGORITHMS, v. 53, n. 1, p. 23-52, JAN 2010. Web of Science Citations: 7.

ANDREANI, ROBERTO; MARTINEZ, J. M.; SVAITER, B. F. A NEW SEQUENTIAL OPTIMALITY CONDITION FOR CONSTRAINED OPTIMIZATION AND ALGORITHMIC CONSEQUENCES. SIAM JOURNAL ON OPTIMIZATION, v. 20, n. 6, p. 3533-3554, 2010. Web of Science Citations: 28.

ANDREANI, R.; CASTRO, S. L. C.; CHELA, J. L.; FRIEDLANDER, A.; SANTOS, S. A. An inexact-restoration method for nonlinear bilevel programming problems. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 43, n. 3, p. 307-328, JUL 2009. Web of Science Citations: 21.

ANDREANI, R.; MARTINEZ, J. M.; MARTINEZ, L.; YANO, F. S. Low Order-Value Optimization and applications. Journal of Global Optimization, v. 43, n. 1, p. 1-22, JAN 2009. Web of Science Citations: 11.

GOMES-RUGGIERO, M. A.; MARTINEZ, J. M.; SANTOS, S. A. SPECTRAL PROJECTED GRADIENT METHOD WITH INEXACT RESTORATION FOR MINIMIZATION WITH NONCONVEX CONSTRAINTS. SIAM JOURNAL ON SCIENTIFIC COMPUTING, v. 31, n. 3, p. 1628-1652, 2009. Web of Science Citations: 16.

ANDRADE, RICARDO; BIRGIN, ERNESTO G.; CHAMBOULEYRON, IVAN; MARTINEZ, JOSE MARIO; VENTURA, SERGIO D. Estimation of the thickness and the optical parameters of several stacked thin films using optimization. APPLIED OPTICS, v. 47, n. 28, p. 5208-5220, OCT 1 2008. Web of Science Citations: 13.

BIRGIN‚ EG; MARTINEZ‚ JM. Improving ultimate convergence of an Augmented Lagrangian method. OPTIMIZATION METHODS & SOFTWARE, v. 23, n. 2, p. 177-195, 2008.

ANDREANI‚ R.; MARTÍNEZ‚ JM; SCHUVERDT‚ ML. On second-order optimality conditions for nonlinear programming. OPTIMIZATION, v. 56, n. 5-6, p. 529-542, 2007.