Computational methods of optimization

• Grant number: 06/53768-0
• Support Opportunities: Research Projects - Thematic Grants
• Start date: October 01, 2006
• End date: September 30, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: José Mário Martinez Perez
• Grantee: José Mário Martinez Perez
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Pesquisadores principais: 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; 09/04785-7 - Automatic differentiation of Hessian matrices, BP.MS; + associated scholarships 09/08027-0 - Global optimization applied to the tomography of quantum states, BP.DR; 09/00576-4 - Dynamic control of infeasibility for inequality constrained optimization, BP.DD; 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

(60)

(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)

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. (04/15635-2, 06/53768-0)

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. (06/03496-3, 06/53768-0, 09/10241-0)

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. (06/53768-0)

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. (06/53768-0, 08/00468-4)

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. (07/06663-0, 06/53768-0, 08/00468-4)

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. (06/53768-0)

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. (07/06663-0, 09/10241-0, 06/53768-0)

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, 2015-12-00. (06/53768-0)

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. (13/07375-0, 06/53768-0)

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. (06/53768-0, 12/10444-0)

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. (06/53768-0, 07/08359-7)

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. (10/18980-3, 10/10133-0, 06/53768-0, 09/10241-0)

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. (06/53768-0, 09/09414-7)

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. (06/53768-0)

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. (06/53768-0)

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. (06/53768-0)

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. (06/53768-0)

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. (06/53768-0, 08/00468-4, 10/16947-9)

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. (06/53768-0)

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. (06/03496-3, 06/53768-0, 09/10241-0)

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. (06/53768-0, 08/00062-8)

MÁRCIA A. GOMES-RUGGIERO; MAEL SACHINE; SANDRA A. SANTOS. 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, 2011-00-00. (06/53768-0, 10/09773-4)

FRANCISCO A. M. GOMES; THADEU A. SENNE. An SLP algorithm and its application to topology optimization. COMPUTATIONAL & APPLIED MATHEMATICS, v. 30, n. 1, p. 53-89, 2011-00-00. (06/53768-0)

MARTINEZ, J. M.; SOBRAL, F. N. C.. Constrained derivative-free optimization on thin domains. Journal of Global Optimization, v. 56, n. 3, p. 16-pg., 2013-07-01. (08/00468-4, 06/53768-0)

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. 13-pg., 2008-10-01. (06/53768-0)

MARTINEZ, JOSE MARIO; PRUDENTE, LEANDRO DA FONSECA. Handling infeasibility in a large-scale nonlinear optimization algorithm. NUMERICAL ALGORITHMS, v. 60, n. 2, p. 15-pg., 2012-06-01. (06/53768-0)

GOWER, R. M.; MELLO, M. P.. A new framework for the computation of Hessians. OPTIMIZATION METHODS & SOFTWARE, v. 27, n. 2, p. 23-pg., 2012-01-01. (06/53768-0, 09/04785-7)

BIRGIN, ERNESTO G.; GENTIL, JAN M.. Evaluating bound-constrained minimization software. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 53, n. 2, p. 27-pg., 2012-10-01. (09/10241-0, 06/53768-0, 06/03496-3)

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. 17-pg., 2011-01-01. (06/53768-0)

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, p. 21-pg., 2011-01-01. (06/53768-0, 01/04597-4)

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. 20-pg., 2011-01-01. (06/53768-0, 10/09773-4)

GOMES, FRANCISCO A. M.; SENNE, THADEU A.. An SLP algorithm and its application to topology optimization. COMPUTATIONAL & APPLIED MATHEMATICS, v. 30, n. 1, p. 37-pg., 2011-01-01. (06/53768-0)

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. (06/53768-0)

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. (06/53768-0)

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. (06/53768-0)

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. (10/09773-4, 06/53768-0)

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. (01/04597-4, 06/53768-0)

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. (06/53768-0)

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. (06/53768-0, 09/04785-7)

BIRGIN‚ EG; MARTINEZ‚ JM. Improving ultimate convergence of an Augmented Lagrangian method. OPTIMIZATION METHODS & SOFTWARE, v. 23, n. 2, p. 177-195, 2008. (06/53768-0)

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. (10/10133-0, 06/53768-0, 09/10241-0, 06/03496-3)

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. (06/53768-0, 09/04785-7)

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. (10/10133-0, 06/53768-0, 09/10241-0)

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. (10/10133-0, 06/53768-0, 09/10241-0)

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. (06/53768-0)

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. (06/53768-0)

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. (06/53768-0)

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. (06/53768-0)

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. (06/03496-3, 06/53768-0)

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. (06/53768-0, 10/19720-5, 09/09414-7)

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. (06/53768-0)

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. (06/53768-0, 01/04597-4)

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. (06/53768-0)

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. (06/53768-0, 07/53471-0, 10/20572-0)

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. (10/10133-0, 06/53768-0, 09/10241-0, 06/03496-3)

ANDREANI‚ R.; MARTÍNEZ‚ JM; SCHUVERDT‚ ML. On second-order optimality conditions for nonlinear programming. OPTIMIZATION, v. 56, n. 5-6, p. 529-542, 2007. (06/53768-0)

ANA FRIEDLANDER; FRANCISCO A. M. GOMES. 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, 2011-00-00. (06/53768-0)

M. A. DINIZ-EHRHARDT; J. M. MARTÍNEZ; L. G. PEDROSO. Derivative-free methods for nonlinear programming with general lower-level constraints. COMPUTATIONAL & APPLIED MATHEMATICS, v. 30, n. 1, p. 19-52, 2011-00-00. (06/53768-0, 04/15635-2)

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. 34-pg., 2011-01-01. (06/53768-0, 04/15635-2)

ANDREANI, ROBERTO; HAESER, GABRIEL; MARTINEZ, J. M.. On sequential optimality conditions for smooth constrained optimization. OPTIMIZATION, v. 60, n. 5, p. 15-pg., 2011-01-01. (06/53768-0)