University of Puerto Rico    (787) 764 0000

    Professor Information

    María D. González-Lima

    Address Department of Mathematics, 17 University Ave. Ste 1701
    San Juan PR, 00925-2537
    Office NCN II C-124
    Hours
    Actual Program
    Telephone (787) 764-0000 88258
    E-Mail ude.rpu@861zelaznog.airam

    Education

    PhD, Rice University, Houston, USA, 1995

    Research Interests

    Applied Mathematics, Numerical Optimization, Models and Applications. Data Mining: Support Vector Machines. Interior Point methods for Mathematical Programming. Large Scale Optimization and low cost algorithms for Machine Learning.

    Selected Publications

    1. F. Arenas, R. Pérez, M. Gonzalez-Lima, C. Arias. A centered Newton method for nonlinear complementarity problems, Journal of Computational and Applied Mathematics, vol. 484, pp. 117473, 2026; https://doi.org/10.1016/j.cam.2026.117473.
    2. M. Gonzalez-Lima, D. W. Barrett, A. Mirji, F. Salehpour, J. R. C. Almeida, F. Gonzalez-Lima. Machine learning prediction of the cognitive responses to transcranial prefrontal photobiomodulation in individuals with bipolar disorder using functional near-infrared spectroscopy, IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 33, pp. 4349-4361, 2025; https://doi: 10.1109/TNSRE.2025.3625855.
    3. M. Campillo, M. Gonzalez-Lima, B. Uribe. A general algorithm for convex fair partitions of convex polygons, Fixed Point Theory Algorithms Sci Eng., Vol. 13, 2024; https://doi.org/10.1186/s13663-024-00769-y.
    4. M. Gonzalez-Lima, C. Ludeña, G. Otazo. A graph classification method based on Support Vector Machines and Locality-Sensitive Hashing. IEEE Access, Vol. 12, pp. 15791-15799, 2024; https://doi.org/10.1109/ACCESS.2024.3356572.
    5. M. Campillo, M. Gonzalez-Lima, B. Uribe. An algorithmic approach to convex fair partitions of convex polygons. MethodsX, Vol. 12, pp. 102530, 2024; https://doi.org/10.1016/j.mex.2023.102530.
    6. R. Barcenas, M. Gonzalez-Lima, J, Ortega, A. Quiroz. On subsampling procedures for Support Vector Machines. Mathematics, Vol. 10, 20, pp. 3776-3796, 2022; https://doi.org/10.3390/math10203776.
    7. M. Gonzalez-Lima, C. Ludeña. Using Locality-sensitive hashing for SVM classification of large data sets. Mathematics, Vol. 10, 11, pp. 1812-1833, 2022; https://doi.org/10.3390/math10111812.
    8. O. Buitrago, A. Ramirez, M. Gonzalez-Lima. Funciones no lineales para la determinaci\'on de un punto interior en la regi\'on factible de problemas de programaci\'on lineal. {Informaci\'on tecnol\'ogica}, Vol. 33, 6, 2022; https://doi.org/10.4067/S0718-07642022000600093.
    9. S. Camelo, M. Gonzalez-Lima, A. Quiroz. Nearest neighbors methods for support vector machines. Annals of Operations Research, Vol. 235, 1, pp. 85-101, 2015.
    10. M. Gonzalez-Lima, D. Oliveira, A. Oliveira. A robust and efficient proposal for solving the linear systems arising in interior-point methods for linear programming. Computational Optimization and Applications, Vol. 56, 3, pp. 573-597, 2013.
    11. M. Gonzalez-Lima, W. Hager, H. Zhang. An affine-scaling interior-point method for continuous knapsack constraints. SIAM Journal on Optimization, Vol. 21, 1, pp. 361-390, 2011.
    12. D. Cores, R. Escalante, M. Gonzalez-Lima, O. Jimenez. On the use of the spectral projected gradient method for support vector machines, Computational and Applied Mathematics, Vol. 28, 3, pp. 327-364, 2009.
    13. M. Gonzalez-Lima, F. Montes de Oca. A Newton-like method for nonlinear system of equations, Numerical Algorithms, Vol. 52, 3, pp. 479-506, 2009.
    14. M. Gonzalez-Lima, H. Wei, H. Wolkowicz. A stable primal-dual approach for linear programming under nondegeneracy assumptions, Computational Optimization and Applications, Vol. 44, 2, pp. 213-247, 2009. (This method is implemented in the software MAPLE.)
    15. M. Gonzalez-Lima. Enhancing the behavior of interior-point methods for linear programming via identification of variables. Optimization Methods \& Software, Vol. 22, pp. 937-958, 2007.
    16. J. Dominguez, M. Gonzalez-Lima. A primal-dual interior-point algorithm for quadratic programming, Numerical Algorithms. Vol. 42, pp. 1-30, 2006.
    17. M. Gonzalez-Lima, C. Roos. On central-path proximity measures in interior point methods. Journal on Optimization Theory and Applications, Vol. 127, 2, pp. 303-328, 2005.
    18. A. Urdaneta, L. Pérez, J. Gómez, B. Feijoo, M. Gonzalez-Lima. Interior point solutions and problems filtering techniques of the coordination problem and directional overcurrent relays. International Journal on Electric Power and Energy Systems, Vol. 23, 8, pp. 819-825, 2001.
    19. M. Gonzalez-Lima, R. Tapia, F. Potra. On effectively computing the analytic center of the solution set, SIAM Journal on Optimization, Vol. 8, 1, pp. 1-25, 1998.
    20. R. Thompson, E. Brinkmann, P. Dharmapala, M. Gonzalez-Lima, R. Thrall. DEA/AR profit ratios and sensitivity of 100 large U.S. banks, European Journal of Operational Research, Vol. 98, pp. 213-229, 1997.
    21. M. Gonzalez-Lima, R. Tapia, R. Thrall. On the construction of strong complementarity solutions for DEA linear programming problems using a primal-dual interior-point method, Annals of Operations Research, Vol. 66, pp. 139-162, 1996.
    22. R. Thompson, P. Dharmapala, J. Diaz, M. Gonzalez-Lima, R. Thrall. DEA analytic center multiplier sensitivity with an illustrative application to independent oil companies, Annals of Operations Research, Vol. 66, pp. 163-177, 1996.

    Grants and Awards

    1. 2025-2027: Learning Prediction Responses to Transcranial Prefrontal PhotoBiomodulation(tPBM) in Bipolar and ADHD Patients using fNIRS, Project FIPI2025-2027. Deanship of Graduate Studies and Research, University of Puerto Rico - Rio Piedras. Principal Investigator. Budget (US $) $23,439.
    2. 2019-2021: A methodology proposal for Support Vector Machines and its use in applications, Project IMP-CIAS-2927. Universidad Militar Nueva Granada, Colombia. Principal Investigator. Budget (US $) $131,778.
    3. 2019-2020: Continuous non linear functions for the solution of linear programming problems, Project INV-ING-2988. Universidad Militar Nueva Granada, Colombia. Co-investigator. Budget (US $) $24,667.
    4. 2018-2019: A methodology proposal for Support Vector Machines in high dimension \& Subsampling and nearest neighbors for nonlinear Support Vector Machines, Projects INV-CIAS 2544 \& 2545. Universidad Militar Nueva Granada, Colombia. Principal Investigator. Budget (US $) $31,500
    5. 2017-2018: Efficient strategies for continous knapsack problems and their application to Support Vector Machines, Project INV-CIAS 2473. Universidad Militar Nueva Granada, Colombia. Principal Investigator. Budget (US $) $27,5000.
    6. 2011 - 2016: Tematic Project 10/06822-4: Efficient solutions of large scale linear and quadratic programming problems, FAPESP- Brasil. Co-investigator. Budget (first four years): Brazilian reals 252,186.02 and (US $) $12,095.
    7. 1999 - 2010: Research Group: CESMa (Center for Statistics and Mathematical Software), Project GID-001, DID (Department of Research and Development of Universidad Sim\'on Bol\'{\i}var). Principal Investigator (years 2004, 2005, 2006). Annual Budgets (US $): $26,446, $25,384, $6,355, $15,307, $11,734, $12,000 $7,248, $7,300, $11,500, $7,000, $6,000.
    8. 1998 - 2002: Development and applications of computational methods to the quantitative analysis of data and models, Project 97000592, Conicit ( National Council for Technology and Sciences). Principal investigator of Subproject AO3: Optimization. Budget (US $): $114,014.
    9. 1996 - 1998: Development of Mathematical Software. Co-investigator. Subproject PAN I, I-06, BID-CONICIT. Approximate Budget (US $): $150,000.

    Additional Information

    • FULBRIGHT/LASPAU Scholarship for studying the Ph.D. July 1990 - August 1993.
    • (OAE) Organization of American States Scholarship. August 1993 - August 1994.
    • National Prize for Excellence in Teaching and Research: CONABA (National Council of Academic Productivity Indices) and CONADES (National Council of Project Development). 1998, 2001. Venezuela.
    • Member of the National System to Promote Research (S.P.I.) Level I. August 1995 to 2003, 2005 to 2011, N- 2450. CONICIT, Venezuela.