Computational Methods in Optimization

• Grant number: 01/04597-4
• Support Opportunities: Research Projects - Thematic Grants
• Start date: August 01, 2001
• End date: July 31, 2005
• 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
• Associated research grant(s): 02/10682-7 - Marcos Raydan | Universidad Central de Venezuela - Venezuela, AV.EXT; 02/10050-0 - Natasa Krejic | University of Novi Sad - Yugoslavia, AV.EXT
• Associated scholarship(s): 04/15635-2 - Derivative-free nonlinear programming, BP.DR

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 main researcher, in the last 22 years. Many works have been developed both in theory and practical aspects of the numerical resolution of nonlinear systems, unconstrained minimization, bound constrained minimization, nonlinear programming, complementarity, variational inequalities and applications. Many M.Sc. and D.Sc. dissertations have been elaborated in the area of the project. Here, we aim to continue the already developed work, in all its aspects. An important difference with respect to previous projects of the group (in particular with respect to the projeto temático 90/03724-6) is that a broad field of applications for numerical methods is included. In fact, we axe currently involved in problems of estimation of parameters in film calculations, and the interest of this work outside Optimization and, even, outside Mathematics, seems very intense. These problems motivate the development of new methods, provide new ideas and challenges and, in general, act as powerful stimula to innovative research. (AU)

Scientific publications

(17)

(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)

BERTOLIM, MARIA ALICE; MELLO, MARGARIDA PINHEIRO; REZENDE, KETTY ABAROA DE. Poincare-Hopf and Morse inequalities for Lyapunov graphs. Ergodic Theory and Dynamical Systems, v. 25, n. 1, p. 1-39, Feb. 2005. (01/04597-4, 02/10246-2, 00/05385-8)

ANDREANI, R.; BIRGIN, E. G.; MARTINEZ, J. M.; SCHUVERDT, M. L.. ON AUGMENTED LAGRANGIAN METHODS WITH GENERAL LOWER-LEVEL CONSTRAINTS. SIAM JOURNAL ON OPTIMIZATION, v. 18, n. 4, p. 1286-1309, 2007. (01/04597-4)

BIRGIN‚ E.G.; CHAMBOULEYRON‚ I.E.; MARTINEZ‚ J.M.; VENTURA‚ S.D.. Estimation of optical parameters of very thin films. APPLIED NUMERICAL MATHEMATICS, v. 47, n. 2, p. 109-119, 2003. (01/04597-4)

BIRGIN‚ EG; SOBRAL‚ FNC. Minimizing the object dimensions in circle and sphere packing problems. Computers & Operations Research, v. 35, n. 7, p. 2357-2375, 2008. (01/04597-4)

MARTÍNEZ‚ J.; MARTINEZ‚ JM. Fitting the Sovová’s supercritical fluid extraction model by means of a global optimization tool. Computers & Chemical Engineering, v. 32, n. 8, p. 1735-1745, 2008. (01/04597-4)

MARTÍNEZ‚ J.M.. Minimization of discontinuous cost functions by smoothing. ACTA APPLICANDAE MATHEMATICAE, v. 71, n. 3, p. 245-260, 2002. (01/04597-4)

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)

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)

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)

BIRGIN, E. G.; MARTÍNEZ, J. M.; RONCONI, D. P.. Optimizing the packing of cylinders into a rectangular container: a nonlinear approach. European Journal of Operational Research, v. 160, n. 1, p. 19-33, Jan. 2005. (01/04597-4, 01/02972-2)

DINIZ-EHRHARDT‚ M.A.; GOMES-RUGGIERO‚ M.A.; LOPES‚ V.L.R.; MARTINEZ‚ J.M.. Discrete Newton’s method with local variations for solving large-scale nonlinear systems. OPTIMIZATION, v. 52, n. 4-5, p. 417-440, 2003. (01/04597-4)

ANDREANI‚ R.; MARTÍNEZ‚ J.M.; MARTÍNEZ‚ L.; YANO‚ F.. Continuous optimization methods for structure alignments. MATHEMATICAL PROGRAMMING, v. 112, n. 1, p. 93-124, 2008. (01/04597-4)

ANDREANI‚ R.; BIRGIN‚ EG; MARTÍNEZ‚ JM; SCHUVERDT‚ ML. Augmented Lagrangian methods under the constant positive linear dependence constraint qualification. MATHEMATICAL PROGRAMMING, v. 111, n. 1, p. 5-32, 2008. (01/04597-4)

BIRGIN‚ E.G.; KREJI{\’C}‚ N.; MARTÍNEZ‚ J.M.. Globally convergent inexact quasi-Newton methods for solving nonlinear systems. NUMERICAL ALGORITHMS, v. 32, n. 2, p. 249-260, 2003. (01/04597-4, 99/03102-0)

BIRGIN‚ EG; MARTÍNEZ‚ JM; NISHIHARA‚ FH; RONCONI‚ DP. Orthogonal packing of rectangular items within arbitrary convex regions by nonlinear optimization. Computers & Operations Research, v. 33, n. 12, p. 3535-3548, 2006. (01/04597-4, 01/02972-2)

ANDREANI‚ R.; MARTINEZ‚ JM; SALVATIERRA‚ M.; YANO‚ F.. Quasi-Newton methods for Order-value optimization and value-at-risk calculations. Pacific Journal of Optimization, v. 2, p. 11-33, 2006. (01/04597-4)

ANDRETTA‚ M.; BIRGIN‚ E.G.; MARTÍNEZ‚ J.M.. Practical active-set Euclidian trust-region method with spectral projected gradients for bound-constrained minimization. OPTIMIZATION, v. 54, n. 3, p. 305-325, 2005. (01/04597-4)