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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, An Inexact newtonInterior-Point Algorithm for Nonlinear Programming,
M. Argaez, J. Hernandez, and L. Velazquez
9)ICIAM Proceedings, 2007, Hybrid optimization approach for solving automated parameter estimation problems, 2007
M. Argaez, H. Klie, C. Quintero, L. Velazquez and M. Wheeler
Pending:
1) Submitted to 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 Computational 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) Submitted to Computational Optimization and Applications:
An Inexact Newton Trust-Region Interior-Point Algorithm for Nonnegative Constrained minimization.
M. Argaez, R. Saenz, and L. Velazquez.
In Preparation:
1) A Hybrid Optimization Algorithm for Parameter Estimation Problems.
M. Argaez, H. Klie, C. Quintero, L. Velazquez, and M. Wheeler.