Optimization, convex analysis, monotone operator theory, splitting algorithms, traffic theory, image processing, Numerical methods for Mean Field Games

Sergio López Rivera, Master of Science, Mathematics. Degree obtained in 2020.
Sergio López Rivera, Mathematical Engineer, obtained in 2020.
Cristian Vega Cereño, Master of Science, Mathematics. Degree obtained in 2020.
Cristian Vega Cereño, Mathematical Engineer, obtained in 2020.

Invited Lectures:

-Splitting algorithms for convex non-smooth optimization, projections, and applications, Seminar of the Department of Management Science and Information Systems, Rutgers Business School, USA, October 2020 (online).
-Splitting algorithms for convex non-smooth optimization, projections, and applications, Nonlinear Analysis seminar of the Department of Mathematics of North Carolina State University, Raleigh USA, September 2020 (online).
-Primal-dual splittings as fixed point iterations in the range of linear operators, Workshop 4 “Nonsmooth Optimization” on the special semester funded by Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, 25 November 2019.
-First order proximal methods in Mean Field Games with local couplings, Workshop on Optimal Control & Mean Field Games, Fundaçao Getulio Vargas, Rio de Janeiro, Brazil, 17 October, 2019.
-Primal-dual splittings as fixed point iterations in the range of linear operators, International Seminar on Optimization and Related Areas, ISORA 2019, IMCA, Lima, Perú, 8 October 2019.
-Mean Field Games with local couplings: numerical approaches, International Conference on Continuous Optimization, ICCOPT 2019, TU, Berlin, Alemania, 6 August 2019.
-Splitting algorithms for convex non-smooth optimization, projections and applications, Séminaire Gipsa-Lab, Université de Grenoble, France, 22 July 2019.
-First order proximal methods in Mean Field Games with local couplings, International Congress in Industrial and Applied Mathematics ICIAM 2019, Valencia, España, 19 July 2019.
-Splitting algorithms for convex non-smooth optimization, projections and applications, Séminaire Laboratoire de Physique, École Normale Supérieure de Lyon, France, 12 July 2019.
-On projecting in primal-dual methods for solving constrained convex optimization, Operator splitting methods in Data Analysis, Flatiron Institute, New York, USA, March 20-22, 2019.
-Projected primal-dual splitting for solving constrained convex optimization, VI Latin American Workshop on Optimization and Control, LAWOC 2018, Escuela Politécnica Nacional, Quito, Ecuador, 3-7 September 2018.
-Forward-Backward-Half Forward Splitting for Solving Monotone Inclusions, International Congress of Mathematicians, ICM2018, Rio Centro, Rio de Janeiro, Brazil, 1-9 August 2018.
-Proximal Methods for Stationary Mean Field Games with Local Couplings: Theory and Algorithms, 18th International Symposium on Dynamic Games and Applications, ENSIMAG, Grenoble, France, 9-12 July 2018.
-Proximal Methods for Stationary Mean Field Games with Local Couplings: Theory and Algorithms, AIMS Conference Series on Dynamical Systems and Differential Equations, Taipei, Taiwan, 5-9 July 2018.
-Projected primal-dual splitting for solving constrained monotone inclusions, XXXI Jornada de Matemática de la Zona Sur, Universidad Austral de Chile, Valdivia, Chile, 25-27 April 2018.
-Splitting Algorithms for Composite Convex Optimization: Acceleration ?, Optimization for Learning Workshop 2018, Universidad Católica de Chile, Santiago, Chile, 18 January 2018.
-Forward-Backward-Half Forward Splitting for Solving Monotone Inclusions, Dynamics and Algorithms in Convex Optimization, DIM-CMM, Universidad de Chile, Santiago, Chile, 14 December 2017.
-Forward-Backward-Half Forward Splitting with non Self-Adjoint linear Operators for Solving Monotone Inclusions, XIII International Seminar on Optimization and Related Areas, Lima, Perú, 12 October 2017.
-Splitting algorithms for solving composite convex optimization problems: A survey and new results, Seminario del Departamento de Estadística e Investigación Operativa, Universidad Complutense de Madrid, España, 8 Septiembre 2017.
-Forward-Backward-Half Forward Splitting with non Self-Adjoint linear Operators for Solving Monotone Inclusions, Mathematical Congress of the Americas 2017, Montréal, Canada, 26 July 2017.
-Proximal splitting algorithms in optimization: A survey and application to Mean Field Games, Séminaire du GdR PHENIX/LIA, Matière: Structure et Dynamique, ENS Lyon, Lyon, France, 11 July 2017.
-Proximal methods for stationary Mean Field Games with local couplings, XXX Jornada de Matemática de la Zona Sur, Universidad Católica de la Santísima Concepción, Concepción, Chile, 26 April 2017.
-Forward-Backward-Half Forward Splitting with non Self-Adjoint linear Operators for Solving Monotone Inclusions, Optimization and Equilibrium: two days workshop, Universidad de Concepción, Concepción, Chile, 25 April 2017.
-Projected Chambolle-Pock splitting for solving monotone inclusions, 5th International Conference on Continuous Optimization (ICCOPT 2016), Tokyo, Japan, 6-11 August 2016.
-Projected Chambolle-Pock splitting for solving monotone inclusions, 28th European Conference on Operational Research (EURO 2016), Poznan, Poland, 3-6 July 2016.
-Strong convergent Tseng's algorithm for solving monotone inclusions, International Symposium on Mathematical Programming (ISMP 2015), Pittsburgh, USA, 12-17 July 2015.
-Strong convergent Tseng's algorithm for solving monotone inclusions, LXXXIII Encuentro Anual de la Sociedad Matemática de Chile, SOMACHI, Quinamávida, Chile, 4-6 December, 2014.
-A splitting method for solving primal-dual monotone inclusions involving vectorial subspaces: application to zero-sum games, 4th Latin American Workshop on Optimization and Control (LAWOC 2014), Lima, Perú, 15-18 July, 2014.
-A splitting method for solving composite primal-dual monotone inclusions involving vectorial subspaces, 12th EUROPT Workshop on Advances in Continuous Optimization, Perpignan, France, 10-12 July, 2014.
-Splitting algorithm for computing Nash equilibria in zero-sum games, XXVII Jornada de Matemática de la Zona Sur, Trailanqui, Temuco, Chile, 23-25 April, 2014.
-The land use planning problem: a primal-dual splitting algorithm, XVI Congreso Chileno de Ingeniería de Transporte, FCFM, Universidad de Chile, Santiago, Chile, 21-25 October 2013.
-Forward-partial inverse-forward method for solving monotone inclusions: application to land use planning, Workshop on Algorithms and Dynamics for Games and Optimization, Playa Blanca, Tongoy, Chile 14-18, October, 2013.
-Forward-partial inverse-forward method for solving monotone inclusions: application to land use planning, XI International Seminar on Optimization and Related Areas, Lima, Peru, 7-11 October 2013.
-Forward-partial inverse-forward method for solving monotone inclusions: application to land use planning, Mathematical Congress of the Americas 2013 (MCA 2013), Guanajuato, Mexico, 5-9 August 2013.
-Forward-partial inverse method for solving monotone inclusions: application to land use planning, International Conference on Continuous Optimization (ICCOPT 2013), Lisbon, Portugal, 27 July -1 August 2013.
-A new error correction technique with strong theoretical properties, International Conference on Continuous Optimization (ICCOPT 2013), Lisbon, Portugal, 27 July -1 August 2013.
-Forward-partial inverse-forward method for solving monotone inclusions: application to land use planning, Workshop Nonlinear Optimization: A Bridge from Theory to Applications, Erice, Sicily, Italy, 10-17 June 2013.
-Méthode explicite-inverse partiel-explicite pour résoudre des inclusions monotones et applications, Journées anuelles du GdR MOA, IHP, Paris, France, 17-19 June 2013.
-Optimal Continuous Pricing with Strategic Consumers, INFORMS Annual Meeting 2012, Phoenix, AZ, USA, 14-17 October, 2012.
-The land use planning problem: a primal-dual splitting algorithm, XVII Congreso Panamericano de Ingeniería de Tránsito, Transporte y Logística (PANAM 2012), U de los Andes, Santiago, Chile, 24-27 September, 2012.
-Preannounced pricing with strategic consumers, International Symposium on Mathematical Programming (ISMP 2012), Berlin, Germany, 19-24 August, 2012.
-Généralisation de la méthode des inverses partielles et de l'éclatement explicite-implicite, Journées du GdR MOA, Hotel le Manganao, Saint François, Guadeloupe, France, 4-7 June, 2012.
-Descomposición monótono+antiadjunto para la resolución de inclusiones monótonas compuestas: aplicación al mercado de uso de suelo, XXV Jornada de Matemática de la Zona Sur, U de Concepción, Chile, 18-20/4/2012.
-Land use equilibrium with general objective functions, 2nd Workshop on Urban Dynamics, URBANICS II, Termas de Chillán, Chile, 26-29 March, 2012.
-A monotone+skew splitting model for composite monotone inclusions in duality, III Latin American Workshop on Optimization and Control, LAWOC 2012, U Técnica Federico Santa María, Valparaíso, Chile,10-13 January, 2012.
-A Douglas-Rachford splitting algorithm for solving equilibrium problems, Septièmes Journées Franco-Chiliennes d'Optimisation, Université de Perpignan Via Domitia, Perpignan, France, 1-3 December, 2011.
-Décomposition de domaine dans les EDP par éclatement d'opérateurs monotones, Journées conjointes GdR MOA et MCPS, La Londe les Maures, France, 6-10 June, 2011.
-A composite fixed point problem and applications, Atelier Franco-Chilien : Dynamiques, Optimisation et Apprentissage, Instituto Sistemas Complejos, Valparaíso, Chile, 22-26 November, 2010.
-Méthode d'éclatement pour la résolution de problems d'équilibre, Conférence annuelle du GdR MOA, Institut Henri Poincaré, Paris, France, 18-20 October, 2010.
-Construction d'équilibres pour un système de problèmes de minimisation, Optimisation : Algorithmes et Dynamique, Laboratoire Arago, Université Pierre et Marie Curie, Banyuls sur Mer, France, 1-2 April, 2010.
-Construction d'équilibres pour un système de problèmes de minimisation, MODE 2010 : Conférence de la SMAI sur l'Optimisation et la Décision, Université de Limoges, Limoges, France, 24-26 March, 2010.
-Convergence d'une méthode de résolution de systèmes d'inclusions monotones couplées, Conférence annuelle du GdR MOA, Porquerolles, France, 18-21 October, 2009.
-Éclatement d'un problème variationnel avec couplage-Application à la décomposition d'images, Congrès SMAI 2009, 4e Biennale Française , La Colle sur Loup, Alpes Maritimes, France, 25-29 May, 2009.
-Un système dynamique discret pour les jeux simultanés faiblement couplés, Dynamic Games, Differential Games III, Roscoff, France, 24-26 November, 2008.
-Un système dynamique discret pour les jeux simultanés faiblement couplés, MODE 2008: Conférence de la SMAI sur l'Optimisation et la Décision, Universtité Blaise Pascal, Clermont-Ferrand, France, 26-28 February, 2008.

Research Visits:

l'École Normale Superieure de Lyon (ENS Lyon), July 2019.
North Carolina State University (NCSU), 22-29 March 2019.
l’Université Paris-Est Marne-la-Vallée (UPEM), June 2018.
l’Université Paris-Saclay, November 2018.
Imperial College de Londres, 21-24 June 2018.
l’École Normale Superieure de Lyon (ENS Lyon), 9-12 July 2017.
l’Université Cergy-Pontoise, 17-31 March 2017.

Event organization:

Session “Optimization and Control” in “Mathematical Congress of the Americas 2017” MCA 2017, Montréal, Canada, 24-28 July 2017.
Congress “8èmes Journées Franco-Chiliennes d’Optimisation” JFCO2017, in honor to Felipe Álvarez, Toulouse, Francia, 5-7 July 2017.
Session “Variational Analysis, Optimization and Applications” in “5º International Conference on Continuous Optimization” ICCOPT2016, Tokyo, Japan, 6-11 August 2016.
Session “Numerical Methods in Optimal Control and Optimization” in “28th European Conference on Operational Research” EURO2016, Poznan, Poland, 3-6 July 2016.
Session “Optimización” in “LXXXIV Encuentro de la Sociedad Matemática de Chile” SOMACHI2015, Pucón, Chile, 26-28 November 2015.

International cooperation projects:

- MathAm Sud 13MATH01, Universidad Técnica Federico Santa María, Associate Researcher, financed by IMPA (Brasil), CONCYTEC (Peru), CONICYT (Chile) and CNRS-INRIA (France), “Variational Analysis and its applications to optimization, monotone operators, convex analysis and Nash equilibrium problems”, 2013-2014.
- ECOS-CONICYT C13E03, Universidad Técnica Federico Santa María, Associate Researcher, “Dynamical systems and algorithms in nonsmooth and nonconvex optimization problems”, financed by CONICYT and CNRS (France), 2014-2015.
- MathAm Sud 15MATH02, Universidad Técnica Federico Santa María, Associate Researcher, “Sparse Optimal Control of Differential Inclusions: Algorithms and Applications”, financed by CONICYT (Chile), SENESCYT (Ecuador), and CNRS (France), 2014-2016.
-Redes 140183, Universidad Técnica Federico Santa María, Associate Researcher, “AM2V-ModeMat Network on Optimization and Control”, financed by CONICYT (Chile) y SENESCYT (Ecuador), 2014-2016.
- Proyecto COSA-INEX-2018, Universidad Cergy Pontoise and Universidad Técnica Federico Santa María, Associate Researcher, “Strategic coordination of autonomous devices: interplay between Information Theory and Game Theory”, 2018-2020.
- Redes 180032, Universidad Técnica Federico Santa María, Associate Researcher, “Stability of optimization and variational systems with applications to natural resources mangement” U. de Chile, University New South Wales (UNSW) and Center for Informatics and Applied Optimisation (CIAO) of Australia, financed by CONICYT (Chile) y UNSW (Australia), 2018-2020.
- ANR JCJC Multisc’In, Associate Researcher, Agence Nationale de la Recherche, France, “Multiscale estimation and Interface detection”, 2020-2023.
- Royal Society Grant, International Exchanges 2020, financed by the Royal Society of UK, "Numerical optimization schemes for gradient flows via Optimal Transport" in collaboration with José Carrillo, Oxford, University, UK.