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http://www.modemat.epn.edu.ec/~jcdelosreyes/
Phone: (+593)2 2976300 Ext. 1531

• PDE-Constrained Optimization
• Bilevel Learning Methods for Imaging and Inverse Problems
• Optimization with Variational Inequality Constraints
• Variational Data Assimilation
• Optimal Control of Non-Newtonian Fluid Flow

• M. D'Elia, J.C. De los Reyes, and A. Miniguano
  Bilevel parameter learning for nonlocal image denoising models.
  Journal of Mathematical Imaging and Vision, to appear. [arXiv:1912.02347]

• J.C. De los Reyes and P. Merino
  An enriched second-order method for nonconvex composite sparse optimization problems.
  MODEMAT Technical Report. [arXiv:2009.01878]

P. Castro, J.C. De los Reyes, S. González, P. Merino

Estimación de parámetros para un modelo del SARS-CoV-2 en Ecuador en presencia de incertidumbre.

Revista Politécnica,

 47(1), 7-16. 

[journal link]

C. Christof, J.C. De los Reyes and C. Meyer
A Nonsmooth Trust-Region Method for Locally Lipschitz Functions with Application to Optimization Problems Constrained by Variational Inequalities.
SIAM Journal on Optimization, 30(3), 2163-2196. [journal link], [arXiv:1711.03208]

• F. Sherry, M. Benning, J.C. De los Reyes, M. Graves, G. Maierhofer, G. Williams, C.-B. Schönlieb and M. Ehrhardt
  Learning the Sampling Pattern for MRI.
  IEEE Transactions on Medical Imaging, Vol. 39(12). [journal link], [arXiv:1906.08754 ]

• P. Castro and J.C. De los Reyes
  A bilevel learning approach for optimal observation placement in variational data assimilation.
  Inverse Problems, Vol. 36(3). [journal link], [arXiv:1811.11505]

• P. Castro, J.C. De los Reyes, S. González, P. Merino. J. Pónce
  Modelización y simulación de la propagación del virus SARS-CoV-2 en Ecuador.
  MODEMAT Technical Report. [report]

• J.C. De los Reyes and D. Villacís
  Bilevel Optimization Methods in Imaging.
  MODEMAT Technical Report.

• J. C. De los Reyes and E. Loayza
  Total generalized variation regularization in data assimilation for Burgers' equation.
  Inverse Problems and Imaging, Vol. 13(4), 755-786. [journal link], [arXiv:1804.04447]

• J.C. De los Reyes
  On the optimal control of some nonsmooth distributed parameter systems arising in mechanics
  GAMM-Mitteilungen, Vol. 40(4), 268-286. [journal link], [arXiv:1711.08418]

• L. Calatroni, J.C. De los Reyes, C.-B. Schönlieb
  Infimal convolution of data discrepancies for mixed noise removal.
  SIAM Journal on Imaging Sciences, Vol. 10(3), 1196-1233. [journal link], [arxiv:1611.00690]

• Cao Van Chung, J.C. De los Reyes and C.-B. Schönlieb
  Learning optimal spatially-dependent regularization parameters in total variation image denoising.
  Inverse Problems, Vol. 33(7). [journal link], [arxiv:1603.09155]

• C.-B. Schönlieb, J.C. De los Reyes and E. Haber
  Preface for Inverse Problems special issue on learning and inverse problems.
  Inverse Problems, Vol. 33(7). [journal link]

• J.C. De los Reyes, E. Loayza and P. Merino
  Second-order orthant-based methods with enriched Hessian information for sparse l1-optimization.
  Computational Optimization and Applications, Vol. 67(2), 225-258. [journal link], [arXiv:1407.1096]

• J.C. De los Reyes, C.-B. Schönlieb and T. Valkonen
  Bilevel parameter learning for higher-order total variation regularisation models.
  Journal of Mathematical Imaging and Vision, Vol. 57(1), 1-25. [journal link], [arxiv:1508.07243]

• L. Calatroni, Cao Van Chung, J.C. De los Reyes, C.-B. Schönlieb and T. Valkonen
  Bilevel approaches for learning of variational imaging models.
  In: Variational Methods in Imaging and Geometric Control, M. Bergounioux, G. Peyré, C. Schnörr, J.-P. Caillau, T. Haberkorn (Eds.), De Gruyter, 2017. [journal link], [arXiv:1505.02120]

• J.C. De los Reyes, R. Herzog and C. Meyer
  Optimal control of static elastoplasticity in primal formulation.
  SIAM Journal on Control and Optimization, Vol. 54(6), 3016-3039. [journal link]

• Juan Carlos De los Reyes and Vili Dhamo
  Error estimates for optimal control problems of a class of quasilinear equations arising in variable viscosity fluid flow.
  Numerische Mathematik, Vol. 132(4), 691-720, 2016. [journal link]

• J.C. De los Reyes and C. Meyer
  Strong stationarity conditions for a class of optimization problems governed by variational inequalities of the second kind.
  Journal of Optimization Theory and Applications, Vol. 108(2), 375-409, 2016. [journal link], [arXiv:1404.4787]

• J.C. De los Reyes, C.-B. Schönlieb & T. Valkonen
  The structure of optimal parameters for image restoration problems.
  Journal of Mathematical Analysis and Applications, Vol. 434(1), 464-500, 2016. [journal link], [arXiv:1505.01953]

• Juan Carlos De los Reyes and Irwin Yousept
  Optimal control of electrorheological fluids through the action of electric fields.
  Computational Optimization and Applications, Vol. 62(1), 241-270, 2015. [journal link]

• Juan Carlos De los Reyes and Georg Stadler
  A nonsmooth model for discontinuous shear thickening fluids: Analysis and numerical solution.
  Interfaces and Free Boundaries, Vol. 16(4), 575-603, 2014. [journal link]

• L. Calatroni, J.C. De los Reyes and C.B. Schönlieb
  Dynamic sampling schemes for optimal noise learning under multiple nonsmooth constraints.
  In: System Modeling and Optimization, C. Poetzsche, C. Heuberger, B. Kaltenbacher, F. Rendl (Eds.), 85-95, Springer-Verlag, 2014. [arXiv:1403.1278]

• L. Kaland, J.C. De los Reyes and N. Gauger
  One shot methods in function space for PDE-constrained optimal control problems.
  Optimization Methods and Software, Vol. 29, 376-405, 2014. [journal link]

• Juan Carlos De los Reyes and Carola-Bibiane Schönlieb
  Image denoising: Learning the noise model via nonsmooth PDE-constrained optimization.
  Inverse Problems and Imaging, Vol. 7(4), 1183-1214, 2013. [journal link]

• J.C. De los Reyes and S. González-Andrade
  Numerical simulation of thermally convective viscoplastic fluids by semismooth second order type methods.
  Journal of Non-Newtonian Fluid Mechanics, Vol. 193, 43-48, 2013. [journal link]

• Juan Carlos De los Reyes
  Optimization of mixed variational inequalities arising in flow of viscoplastic materials.
  Computational Optimization and Applications, Vol. 52, 757-784, 2012. [journal link]

• Juan Carlos De los Reyes and Sergio González-Andrade
  A combined BDF-semismooth Newton approach for time dependent Bingham flow.
  Numerical Methods for Partial Differential Equations, Vol. 28, 834-860, 2012. [journal link]

• Juan Carlos De los Reyes
  Optimal control of a class of variational inequalities of the second kind.
  SIAM Journal on Control and Optimization, Vol. 49, 1629-1658, 2011. [journal link]

• Juan Carlos De los Reyes and Michael Hintermüller
  A duality based semismooth Newton framework for solving variational inequalities of the second kind.
  Interfaces and Free Boundaries, Vol. 13, 437-462, 2011. [journal link]

• J.C. De los Reyes and T. Stykel
  A balanced truncation based strategy for optimal control of evolution problems.
  Optimization Methods and Software, Vol. 26, 671-692, 2011. [journal link]

• Juan Carlos De los Reyes
  On the optimization of steady Bingham flow in pipes.
  In: Recent Advances in Optimization and its Applications in Engineering, M. Diehl, F. Glineur, E. Jarlebring and W. Michiels (Eds.), 379-388, Springer Verlag, 2010.

• Juan Carlos De los Reyes and Sergio González-Andrade
  Numerical simulation of two-dimensional Bingham fluid flow by semismooth Newton methods.
  Journal of Computational and Applied Mathematics, Vol. 235, 11-32, 2010. [journal link]

• Juan Carlos De los Reyes and Karl Kunisch
  Optimal control of partial differential equations with affine control constraints.
  Control and Cybernetics, Vol. 38, 1217-1250, 2009. [journal link]

• Juan Carlos De los Reyes and Irwin Yousept
  Regularized state-constrained boundary optimal control of the Navier-Stokes equations
  Journal of Mathematical Analysis and Applications, Vol. 356, 257-279, 2009. [journal link]

• Juan Carlos De los Reyes and Sergio González-Andrade
  Path-following methods for steady laminar Bingham flow in cylindrical pipes
  ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 43, 81-117, 2009. [journal link]

• Juan Carlos De los Reyes and Karl Kunisch
  On some nonlinear optimal control problems with vector-valued affine control constraints.
  In: Optimal Control of Coupled Systems of PDE, K. Kunisch, J. Sprekels, G. Leugering, F. Tröltzsch (Eds.), 105-122, Birkhäuser, 2009. [chapter link]

• E. Casas, J.C. De los Reyes and F. Tröltzsch
  Sufficient second-order optimality conditions for semilinear control problems with pointwise state constraints.
  SIAM Journal on Optimization, Vol. 19, 616-643, 2008. [journal link]

• Juan Carlos De los Reyes, Christian Meyer and Boris Vexler
  Finite element error analysis for state-constrained optimal control of the Stokes equations.
  Control and Cybernetics, Vol. 37, 251-284, 2008. [journal link]

• J.C. De los Reyes and R. Griesse
  State-constrained optimal control of the three-dimensional stationary Navier-Stokes equations.
  Journal of Mathematical Analysis and Applications, Vol. 343, 257-272, 2008. [journal link]

• J.C. De los Reyes, P. Merino, J. Rehberg and F. Tröltzsch
  Optimality conditions for state-constrained PDE control problems with time-dependent controls.
  Control and Cybernetics, Vol. 37, 5-38, 2008. [journal link]

• Juan Carlos De los Reyes and Irwin Yousept
  Boundary optimal flow control with state constraints.
  Proceedings in Applied Math. and Mechanics, Vol. 7, 2060029-2060030, 2008.

• J.C. De los Reyes and F. Tröltzsch
  Optimal control of the stationary Navier-Stokes equations with mixed control-state constraints.
  SIAM Journal on Control and Optimization, Vol. 46, 604-629, 2007. [journal link]

• A. Carnarius, J. C. De los Reyes, B. Günther, F. Thiele, F. Tröltzsch, D. Wachsmuth
  Numerical study of the optimization of separation control.
  AIAA Paper 2007-0058, 2007. [paper link]

• J. C. De los Reyes and F. Tröltzsch
  Flow control with regularized state constraints.
  In: Active Flow Control, R. King (Ed.), 353-366, Springer Verlag, 2007. [chapter link]

• J.C. De los Reyes and K. Kunisch
  A semi-smooth Newton method for regularized state-constrained optimal control of the Navier-Stokes equations.
  Computing, Vol. 78, 287-309, 2006. [journal link]

• J.C. De los Reyes
  Primal-dual active set method for control constrained optimal control of the Stokes equations.
  Optimization Methods and Software, Vol. 21, 267-293, 2006. [journal link]

• J.C. De los Reyes and K. Kunisch
  A semi-smooth Newton method for control constrained boundary optimal control of the Navier-Stokes equations.
  Nonlinear Analysis: Theory, Methods and Applications, Vol. 62, 1289-1316, 2005. [journal link]

• J.C. De los Reyes
  A primal-dual active set method for bilaterally control constrained optimal control of the Navier-Stokes equations.
  Numerical Functional Analysis and Optimization, Vol. 25, 657-683, 2004. [journal link]

• J.C. De los Reyes and K. Kunisch
  A comparison of algorithms for control constrained optimal control of the Burgers equation.
  Calcolo, Vol. 41, 203-225, 2004. [journal link]

• J.C. De los Reyes
  A SQP method for constrained optimal control of the Burgers equation.
  I+D Innovación, Vol. 13, 115-129, 2004.

• Juan Carlos De los Reyes
  Constrained Optimal Control of Stationary Viscous Incompressible Fluids by Primal-Dual Active Set Methods.
  PhD Thesis, Karl-Franzens University of Graz, 2003.

• Juan Carlos De los Reyes
  Localización óptima de instalaciones: una aplicación a los servicios de emergencia
  Diploma Thesis, EPN Quito, 2000

• Modelización de la propagación del SARS-CoV-2 en Ecuador
• Modelización matemática y control de fluidos magneto- y electro-reológicos
• Restauración de imágenes mediante un esquema de optimización con operadores no locales
• Sparse Optimal Control of Differential Equations: Algorithms and Applications
• Sparse Optimization Techniques for Data Assimilation in Numerical Weather Prediction
• Optimización de parámetros reológicos de flujos volcánicos a partir de imágenes de alta resolución
• Asimilación de datos satelitales e in-situ para modelos de predicción de oleaje para la costa ecuatoriana
• Métodos de optimización para la identificación computacional del tipo de ruido en imágenes médicas
• Control óptimo del problema de dos fases de Stefan en su formulación de entalpía
• Mathematical Modeling and Numerical Simulation of Shear Thickening Fluids
• Optimal Control of Variational Inequalities of the Second Kind
• Numerical Simulation of Visco-plastic Fluids
• Simulación numérica y control de mezclas en el acoplamiento de tuberías
• Constrained Optimal Control of the Navier-Stokes Equations