Marcos
Raydan
Publications: Books: Métodos Iterativos tipo Krylov para Sistemas Lineales, Ed: Centro de Estudios Avanzados, Instituto de Investigaciones Científicas (IVIC), Caracas, Venezuela, (with B. Molina), (2004). ISBN: 980261078X. Alternating Projection Methods, SIAM, (with René Escalante), (2011). ISBN 9781611971934. Papers: • Inexact Newton's method with inner implicit preconditioning for algebraic Riccati equations, Computational and Applied Mathematics, to appear, (2016) (con JeanPaul Chehab). • Geometrical inverse preconditioning for symmetric positive definiite matrices, Mathematics, Vol. 4, 46, doi:10.3390/math4030046, (2016) (with JeanPaul Chehab). • Inversefree recursive multiresolution algorithms for a data approximation problem, Computers and Mathematics with Applications, Vol. 72, 11771187, (2016) (with M. A. Fortes and A. M. SajoCastelli). • An acceleration scheme for Dykstra's algorithm, Computational Optimization and Applications, Vol. 63, 2944, (2016), (with Williams López). • An innerouter nonlinear programming approach for constrained quadratic matrix model updating, Mechanical Systems and Signal Processing, Vol. 6667, 7888, (2016) (with M. Andretta and E. Birgin). • Separable cubic modeling and a trustregion strategy for unconstrained minimization with impact in global optimization, Journal of Global Optimization, Vol. 63, Issue 2, 319342, (2015) (with J. M. Martínez). • Preconditioned conjugate gradient method for finding minimal energy surfaces on Powell  Sabin triangulations, Journal of Computational and Applied Mathematics, Vol. 268, 3455, (2014)
(with A. M. SajoCastelli y M. A. Fortes). • Spectral Projected Gradient methods: Review and Perspectives, Journal of Statistical Software, Vol. 60, Issue 3, (2014) (with Ernesto Birgin and J. M. Martínez). • Pseudoinverse preconditioners and iterative methods for large dense linear leastsquares problems, Bulletin
of Computational Applied Mathematics, Vol. 1, 2547,
(2013) (with Oskar Cahueñas and Luis M. HernándezRamos)• On the geometrical structure of symmetric matrices, Linear Algebra and its Applications, Vol. 438, 12011214, (2013) (with Roberto Andreani and Pablo Tarazaga). • A hybridoptimization method for largescale nonnegative full regularization in image restoration, Inverse Problems in Science & Engineering, Vol. 21, 741766 (2013), (with Johana Guerrero and Marielba Rojas).
• Newton's method and secant methods: A longstanding relationship from vectors to matrices, Portugaliae Mathematica, Vol. 68, 431475 (2011) (with Marlliny Monsalve). • Unconstrained optimization techniques for the acceleration of alternatingprojection methods, Numerical Functional Analysis and Optimization, Vol. 32, 10411066 (2011) (with Luis M. HernándezRamos and R. Escalante). • An implicit preconditioning strategy for largescale generalized Sylvester equations, Applied Mathematics and Computation, Vol. 217, 87938803 (2011) (with JeanPaul Chehab). • Convex constrained optimization
for largescale generalized Sylvester equations, Computational Optimization and Applications, Vol. 48, 233253 (2011) (with A. Bouhamidi and
K. Jbilou).
• A
secant method for nonlinear matrix problems, Special Volume in Numerical Linear Algebra in Signals, Systems
and Control, Springer, Series: Lecture Notes in Electrical Engineering,
Vol. 80, Van Dooren, P.; Bhattacharyya, S. P.; Chan, R. H.;
Olshevsky, V.; Routray, A. (Eds.), Chapter 19 (2011) (with Marlliny Monsalve).
• Computing a
nearest correlation matrix with factor structure,
SIAM J. Matrix Analysis and Applications, Vol. 31, 26032622 (2010) (with Rüdiger Borsdorf
and Nicholas J. Higham).
• Residual methods for the largescale
matrix pth root and some related problems, Applied Mathematics and Computation, Vol. 217, 650660 (2010) (with Braulio
De Abreu).
• Residual algorithm for largescale
generalized eigenvalue problems, Computational Optimization and Applications, Vol. 46, 217227 (2010)
(with Lenys Bello and William La Cruz).
• A
new inversionfree method for a rational matrix equation,
Linear Algebra and its Applications, Vol. 433, 6471
(2010) (with Marlliny Monsalve).
• Implicitly preconditioned and globalized residual method
for solving steady fluid flows, Electronic Transactions
on Numerical Analysis (ETNA), Vol. 34, 136151, (2009) (with
Jean Paul Chehab).
• A symmetry preserving alternating
projection method for matrix model updating, Mechanical
Systems and Signal Processing, Vol. 23, 17841791, (2009)
(with Joali Moreno and Biswa Datta). • Dykstra's algorithm and robust stopping criteria,
in: Encyclopedia of Optimization, Second Ed., Editors: C. A.
Floudas and P. M. Pardalos, Part 4, pp. 828833, (2009) (with Ernesto Birgin). ISBN:9780387747590. • Spectral Projected Gradient Methods, in: Encyclopedia of Optimization, Second Ed., Editors: C. A. Floudas and P. M. Pardalos, Part 19, pp. 36523659, (2009) (with E. Birgin and J. M. Martínez). ISBN: 9780387747590.
•
Geometrical properties of the Frobenius condition number for
positive definite matrices, Lineal Algebra and its Applications,
Vol. 429, pp. 20892097, (2008) (with Jean Paul
Chehab).
• Specialized and
hybrid Newton schemes for the matrix pth root,
Applied Mathematical Sciences, Vol. 2, No. 49, pp. 24012424,
(2008) (with B. De Abreu and M. Monsalve).
• Residual iterative schemes
for largescale nonsymmetric positive definite linear systems,
Computational and Applied Mathematics, Vol. 27,
pp. 151173, (2008) (with William La Cruz).
• A derivativefree tolerant
line search technique for unconstrained optimization, Journal
of Computational and Applied Mathematics, Vol. 219, pp. 383397,
(2008) (with M. A. DinizEhrhardt and J. M. Martínez).
• On the solution of the symmetric
eigenvalue complementarity problem by the spectral projected
gradient algorithm, Numerical Algorithms, Vol. 47,
pp. 391407, (2008) (with J.J. Judice, S. Rosas and S. Santos).
• ConvexConstrained Optimization
for the Seismic
Reflection Tomography Problem, Journal
of Applied Geophysics, Vol. 62, pp. 158166, (2007)
(with Lenys Bello).
• Spectral Projected Subgradient
with a Momentum Term for the Lagrangean Dual Approach, Computers and Operations Research, Vol. 34, pp. 31743186, (2007) (with A. Crema
and M. Loreto).
•
CauchySchwarz and Kantorovich type Inequalities for Scalar
and Matrix Moment Sequences, Advances in Computational
Mathematics, Vol. 26, pp. 7180, (2007) (with Claude Brezinski).
• Spectral Residual Method without
Gradient Information for Solving LargeScale Nonlinear Systems
of Equations, Mathematics of Computation,
Vol. 75, pp. 14491466, (2006) (with W. La Cruz
and J. M. Martínez). [Pdf
file] [Fortran
Code]
• Implicit and Adaptive Inverse
Preconditioned Gradient Method for Nonlinear Problems,
Applied Numerical Mathematics, Vol. 55, pp. 3247, (2005)
(with Jean Paul Chehab).
• Preconditioned Spectral Projected
Gradient Methods on Convex Sets, Journal of Computational
Mathematics, Vol. 23, pp. 225232 (2005) (with Lenys Bello).
• Robust Stopping Criteria for
Dykstra's Algorithm, SIAM J. Sci. Comp., Vol. 26,
pp. 14051414, (2005) (with Ernesto Birgin).
• Spectral Gradient Methods for
Linearly Constrained Optimization, Journal
of Optimization Theory and Applications, Vol. 125, pp. 629651
(2005) (with J. M. Martínez and E. Pilotta).
• Low Cost Methods
for Nonlinear LargeScale Matrix Equations,
in Y. Yuan, ed., Numerical Linear Algebra and Optimization, (Science
Press, Beijing), pp.7987 (2004).
• Nonmonotone Spectral Methods
for LargeScale Nonlinear Systems, Optimization
Methods and Software, Vol. 18, pp. 583599 (2003)
(with William La Cruz). [Fortran
Code]
• Gradient
Method with Dynamical Retards for LargeScale Optimization Problems,
Electronic Transactions on Numerical Analysis (ETNA), Vol. 16,
pp. 186193 (2003) (with Francisco Luengo).
• Inexact Spectral Projected
Gradient Methods on Convex Sets, IMA
Journal of Numerical Analysis, Vol. 23, pp. 539559 (2003)
(with Ernesto Birgin and J. M. Martínez).
• Selective
Alternating Projections to Find the Nearest SDD+ Matrix,
Applied Mathematics and Computation, Vol. 145, pp. 205220 (2003)
(with M. Monsalve, J. Moreno and R. Escalante).
• Smooth and Adaptive
Gradient
Method with Retards, Mathematical
and Computer Modelling, Vol. 36, pp. 11611168 (2002) (with J.
L. Lamotte and B. Molina).
• Preconditioned Spectral Gradient
Method, Numerical Algorithms, Vol. 30, pp. 241258 (2002) (with
F. Luengo, W. Glunt and T.L. Hayden).
• Primal
and Polar Approach for Computing the Symmetric Diagonally Dominant
Projection,
Numerical Linear Algebra with Applications, Vol. 9, pp. 333345
(2002), (with Pablo Tarazaga).
• Spectral Variants of Krylov
Subspace Methods, Numerical Algorithms, Vol. 29, pp. 197208
(2002), (with Brigida Molina).
• Relaxed Steepest Descent and
CauchyBarzilaiBorwein Method, Computational Optimization and Applications, Vol. 21, pp. 155167
(2002), (with
Benar Svaiter).
• Algorithm 813: SPG  Software
for ConvexConstrained Optimization, ACM Transactions on Mathematical Software, Vol. 27, pp. 340349
(2001), (with
E. G. Birgin and J. M. Martínez).
• PerronFrobenius Theorem for
Matrices with Some Negative Entries, Linear Algebra and its Applications, Vol. 328, pp. 5768 (2001),
(with Pablo
Tarazaga and Ana Hurman).
• Low
Cost Optimization Techniques for Solving the Nonlinear Seismic
Reflection Tomography Problem,
Optimization and Engineering, Vol. 1, pp. 155169 (2000), (with
Z. Castillo and Debora Cores).
• An Assesment of
the Preconditioned Gradient
Method with Retards for Parallel Computers, Computational and Applied
Mathematics, Vol. 19, pp. 323337, (2000), (with B. Molina and
S. Petiton).
• Theoretical
Analysis of Exponential Transversal Method of Lines for the Diffusion
Equation,
Numerical Methods for Partial Differential Equations, Vol. 12,
pp. 3042, (2000), (with Abraham Salazar and Antonio Campo).
• Nonmonotone Spectral
Projected Gradient Methods on Convex Sets, SIAM Journal
on Optimization, Vol.10, pp. 11961211, (2000), (with E. G. Brigin
and J.M. Martínez).
• Computing the Symmetric
Diagonally Dominant Projection via Duality, Proceedings of the
XV Interuniversity Mathematical Research Seminar (XV SIDIM), University
of Puerto Rico, Mayaguez Campus, Puerto Rico, pp. 5976, (2000),
(with Pablo Tarazaga).
• Gradient
Method with Retards and Generalizations, SIAM Journal on Numerical
Analysis, Vol. 36, pp. 275289, (1999), (with Ana Friedlander,
J. M. Martínez and B. Molina).
•
Computing the Nearest Diagonally Dominant Matrix,
Numerical Linear Algebra with Applications, Vol. 5, pp. 461474,
(1998), (with Maria Mendoza and Pablo Tarazaga).
• Dykstra's Algorithm
for Constrained LeastSquares Rectangular Matrix Problems,
Computers and Mathematics
with Applications, Vol. 35, pp. 7379, (1998), (with Rene Escalante).
• An Adaptive Algorithm
for Bound Constrained Quadratic Minimization,
Investigacion Operativa,
Vol. 7, pp. 67102, (1997), (with R. H. Bielschowsky, Ana Friedlander,
F. M. Gomes and J. M. Martínez).
• Preconditioned
Gradient
Method with Retards for Parallel Computers, Proceedings of the III
National Meeting on Parallel and Distributed Computing, Merida,
Venezuela, pp. 9198, (1997), (with B. Molina and S. Petiton).
• The Barzilai and
Borwein Gradient Method for the LargeScale Unconstrained Minimization
Problem,
SIAM Journal on Optimization,
Vol. 7, pp. 2633, (1997).
• Theoretical
Analysis of Exponential Transversal Method of Lines for the Diffusion
Equation,
Proceedings of the
31st National Heat Transfer Conference, Houston, Texas, USA, ASME
Publications, Vol. 331, pp. 95102, (1996), (with
Abraham Salazar and Antonio Campo).
• Dykstra's Algorithm
for a Constrained LeastSquares Matrix Problem,
Numerical Linear Algebra
with Applications, Vol. 3, pp. 459471, (1996), (with Rene Escalante).
• The Preconditioned
BarzilaiBorwein Method for the Numerical Solution of Partial
Differential Equations,
Numerical Algorithms,
Vol. 13, pp. 4560, (1996), (with B. Molina).
• A New Method for
LargeScale Box Constrained Convex Quadratic Minimization Problems,
Optimization Methods
and Software, Vol. 5, pp. 5774, (1995), (with Ana Friedlander
and J. M. Martínez).
• Preconditioners
for Distance Matrix Algorithms,
Journal of Computational
Chemistry, Vol. 15, pp. 227232, (1994), (with W.
Glunt and T.L. Hayden).
• Exact Order of
Convergence of the Secant Method,
Journal of Optimization
Theory and Applications, Vol. 78, pp. 541551, (1993).
• Molecular Conformations
from Distance Matrices,
Journal of Computational
Chemistry, Vol. 14, pp. 114120, (1993), (with W.
Glunt and T.L. Hayden).
• On the Barzilai
and Borwein Choice of Steplength for the Gradient Method,
IMA Journal of Numerical
Analysis, Vol. 13, pp. 321326, (1993).
• A General Algorithm
in Optimal Control Problems,
Acta Cientifica Venezolana,
Vol. 40, pp. 174180, (1989), (with José Aguilera).
• Comparison of Several
Codes for Solving Large Sparse Linear Systems,
Acta Cientifica Venezolana,
Vol. 36, pp. 100102, (1985), (with H. Lopez, C.
Maulino, V. Pereyra and A. Sanchez).
