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Research:
Hybrid optimization methods for large scale nonlinear programs
Research Grants:
Army High-Performance Research Center,2007-2012 with HTPi and Stanford
NSF CyberSHare Center, 2007-2012, with Geological and Computer Science Depts.
NSF NEERS Grant, 2006-2010, with Carnegie Mellon, UC-San Diego, UT-Austin
MSU PET Grant, 2006-2008 with UT-Austin
Papers:
A global optimization technique with applications to the phase-retrieval problem in X-ray crystallography.
G.N. Phillips Jr., R.A. Tapia, L. Velžzquez, and Y. Zhang.
2) Journal of Optimization Theory and Applications, Vol. 107 (3): 529-546, December 2000:
On convergence of minimization methods: attraction, repulsion and selection.
Y. Zhang, R.A. Tapia, and L. Velazquez
3) Computational Optimization and Applications: An International Journal, Vol. 20 (3): 299-315, December 2001:
Selective search for global optimization of zero or small residual least-squares problems: a numerical study.
L. Velazquez, G.N. Phillips, Jr., R.A. Tapia, and Y. Zhang.
4) Journal of Optimization Theory and Applications, Vol. 114 (2):, August 2002:
Numerical comparisons of path-following strategies for a primal-dual interior-point method for nonlinear programming.
M. Argaez, R.A. Tapia, and L. Velazquez.
5) Association of Computing Machinery: Proceedings of the 2003 conference on Diversity in Computing, October 2003:
A New Infeasible Primal-Dual Interior-Point Algorithm for Linear Programming.
M. Argaez and L. Velazquez.
6)Association of Computing Machinery: Proceedings of the 2003 Conference on Diversity in Computing, October 2003:
On the Development of Interior-Point Trust-Region Methods for Large Scale Nonlinear Programming Problems.
M. Argaez, L. Velazquez, and C. Villalobos.
7)Association of Computing Machinery and IEEE-CS: Proceedings of the 2005 Conference on Dive
rsity in Computing, October 2005:
On a Global Optimization Method for a Nonlinear Hyperboloid Least Squares Problem
.
L. Velazquez, M. Argaez, B. Bueno and B. Stec.
8)Revista Colombiana de Matematicas, Vol. 41, Suppl.1, pp. 197-220, Print ISSN 0034-7426,2006:
An Inexact Newton
Interior-Point Algorithm for Nonlinear Programming,
M. Argaez, J. Hernandez, and L. Velazquez
9)PAMM Journal, ICIAM Proceedings,Vol. 7,Pages 1062507 - 1062508, December 2007,DOI: 10.1002/pamm.200700948:
Hybrid optimization approach for solving automated parameter estimation problems,
M. Argaez, H. Klie, C. Quintero, L. Velazquez and M. Wheeler
10) 26th Army Science Conference Proceedings, Dec. 2009:
Numerical Testing of Parameterization Schemes for solving parameter estimation problems,
L. Velazquez, M. Argaez, C. Quintero, H. Klie, and M.F. Wheeler.
11)IEEE Transactions on Signal Processing, Vol. 56, No, 6, June 2009, ISSN 1053-587X:
Compressive Sensing Reconstruction with Prior Information by Iteratively Reweighted Least-Squares, C.J. Miosso, R. von Borries, M. Argaez, L. Velazquez, Cquintero, and C.M. Potes
Pending:
1) Submitted to European Biophysical Journal:
Detecting Allosteric Transition by the change in Parameters of the Hyperboloid Fitted to the Beta Sheet Region of Selected Allosteric Enzymes.
E. Tolonen, B. Bueno, S. Kulshreshta, M. Argaez, L. Velazquez, and B. Stec.
2) Submitted to SIAM Journal on Optimization:
On the Use of the Quasicentral Path in an Infeasible Interior-Point Method for Linear Programming.
M. Argaez, O. Mendez, and L. Velazquez.
3) Technical Report
An Inexact Newton Trust-Region Interior-Point Algorithm for Nonnegative Constrained minimization.
M. Argaez, R. Saenz, and L. Velazquez.
In Preparation:
1) Numerical Comparison of Constrained Optimization Schemes for Solving Earthquake Modeling Problems,
L. Velazquez, C. Burstede, U.A. Sosa-Aguirre, M. Argaez, and O. Ghattas.