Nonconvex optimization: scalar & vector; Calculus of variations: asymptotic analysis; Nonconvex quadratic optimization; Nonsmooth analysis.

Theses awarding the degree in Mathematical Engineering (Universidad de Concepción).
1.``Algoritmos Numéricos para la Resolución del Problema del Regulador Lineal'', Lorena Muñoz. December 1995.
2.``Selecciones regulares para el subdiferencial de una función convexa y aplicaciones'', Victor Puchi. March 1997.
3.``Un resultado tipo Liapunov en Cálculo de Variaciones'', Verónica Briceño. May 1998.
4.``Eficiencia en Optimización multiobjetivo no convexa'', Felipe Ignacio Lara Obreque. October 2010.
5.``Dualidad Fuerte en Optimización No Convexa'', Gabriel Cárcamo Aravena. April 2012.
6.``Análisis asintótico de segundo orden para el problema de minimización'', Iván Andrés Montenegro Gómez. July 2014.
7. ``Convexidad de rango cuadrático en bajas dimensiones y aplicaciones en optimización cuadrática”, Felipe Andrés Opazo Lagos. December 2015.
8. ``Una revisión de la teoría dualidad Lagrangiana con aplicaciones en optimización cuadrática non convexa”, Stephanie Paola Caro Torres. October 21, 2016.
9. ``Una nueva clase de problemas cuasiconvexos con gap de dualidad cero”, Filip Agustín Thiele Guerrero. September 27, 2019.
10.``Optimización cuadrática sobre una restricción intervalar con incertidumbre'', Ariel Esteban Pérez Almonacid, March 22, 2021.
11.``Eficiencia en optimización multiobjetivo: resultados analíticos y algorítmicos'', Yamira Isabel Roa Céspedes, May 21, 2021.

Theses awarding the Master in Mathematics (Universidad de Concepción).
1.``Vector equilibrium problems involving moving cones'', Fernando Flores Bazán. Defense on November 30, 2001.
2. ``On the representation of the $\varepsilon$-$\Phi$-Subdifferential for a class on $\Phi$-convex functions with applications'', Dante Carrasco Olivera. Defense on November 29, 2002.
3. ``Dualidad Fuerte en Optimización No Convexa y Aplicaciones”, Máximo Florean Chávez Santos: Facultad de Ciencias - IMCA, Universidad Nacional de Ingeniería, Lima, Perú. Defense on July 16, 2019.

Theses awarding the PhD in Applied Sciences (Departamento de Ingeniería Matemática, Universidad de Concepción)
1. ``Asymptotic Analysis in Equilibrium Problems'', Rubén López Montoya. Defense on January 07, 2005.
2.``Existence and Optimality Conditions in Nonconvex Vector Optimization'', Cristián Vera Donoso. Defense on March 15, 2006.
3.``Second Order Asymptotic Analysis in Optimization'', Felipe Ignacio Lara Obreque. Defense on October 14, 2015.
4.``Strong Duality in Nonconvex Optimization and Related Properties'', Gabriel Cárcamo Aravena. Defense on November 29, 2018.
5.``A Theoretical Framework for the Environmental/Economical Dispatch Problem'', Adrian Carrillo Galvez. Defense on January 27, 2022.

Theses awarding the PhD in Mathematics (Departamento de Matemática, Universidad de Concepción)
6.``Some Problems in Nonconvex Optimization'', Luis González. Defense on March 15, 2023

1. Invited talks (2015 ->):
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* Series of ten lectures (two hours each), as a short course, entitled “Vector Optimization”, delivered at Departamento de Gestión y Control de la Facultad de Economía y Negocios de la Universidad de Chile, Santiago-Chile, January 14 - 16; 21 - 23, 2015.
* "Strong duality in nonconvex optimization with a single equality and geometric constraints: applications to QP”, invited talk delivered at Dipartimento di Informatica, Università di Pisa, Pisa-Italy, 30 June, 2015.
* “A unifying model in vector optimization theory”, invited talk delivered at Departamento de Matemática Aplicada I, Escuela Técnica Superior de Ingeniería Industriales, Universidad Nacional de Educación a Distancia, Madrid-Spain, 09 July, 2015.
* “Lagrangian duality without standard convexity”, Series of five lectures (three hours each) delivered at Instituto de Matemática y Ciencias Afines (IMCA), Universidad Nacional de Ingeniería, Lima - Perú, 04 - 10 February, 2016.
* “Introduction to Calculus of Variations”, Series of five lectures (three hours each) delivered at Instituto de Matemática y Ciencias Afines (IMCA), Universidad Nacional de Ingeniería, Lima - Perú, 13 - 19 April, 2016.
* “A semi-infinite programming approach fo rthe circular conic STQOP: strong duality, optimality and hidden convexity”, invited talk delivered at Dipartimento di Informatica, Università di Pisa, Pisa-Italy, 04 July, 2016.
* “Does convexity arise in optimization naturally?”, Invited talk delivered at Center for Mathematical Modeling (CMM), Universidad de Chile, Santiago, 16 November, 2016.
* “De la Optimización a la teoría de juegos no-cooperativos: un recuento interesante”, Invited conference delivered at Facultad de Ciencias, Universidad Nacional de Ingeniería, Lima - Perú, 05 February, 2018.
* “Characterizing efficiency on infinite-dimensional commodity spaces with ordering cones having possibly empty interior”, Invited talk delivered at Centro de Investigación (CIUP), Universidad del Pacífico, Lima - Perú, 16 August, 2019.
* “Optimizando durante toda la vida: un recuento interesante”, Invited talk delivered at Área de Matemática, Facultad de Ciencias, Dirección General de Investigación de la Vicerrectoría de Investigación, Innovación y Postgrado, Universidad Arturo Prat, Iquique - Chile, 04 Septiembre, 2019.
* “Convexity of images for quadratic-linear mappings and applications”, invited talk delivered at Departamento de Matemática Aplicada I, Escuela Técnica Superior de Ingeniería Industriales, Universidad Nacional de Educación a Distancia, Madrid-Spain, 19 November, 2019.
* “Escalarizacion lineal y no lineal en optimización no convexa”, invited talk delivered at Escuela Técnica Superior de Ingeniería de Telecomunicación, Campus Miguel Delibes, Universidad de Valladolid, Spain, 25 November, 2019.
* “Quasiconvexity of the minimum of any translation of quasiconvex functions: some consequences for their sum and applications”, Invited talk delivered at Departamento de Matemática, Universidad de Tarapacá, Arica - Chile, 10 September, 2020. (Virtual)

2. Plenary/Invited speaker (2015 ->)
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* “Geometric and topological characterization of strong duality in nonconvex optimization”, Plenary conference at International Conference on Variational Analysis, Optimization and Quantitative Finance (honoring Terry Rockafellar’s 80th birthday, University of Limoges, Limoges-Francia, May 18-22, 2015.
* “Searching convexity in nonconvex optimization”, Plenary conference delivered in occasion of the XXIV Congreso de Matemática Capricornio (COMCA), Campus Playa Brava, Universidad Arturo Prat, Iquique-Chile, August 05-07, 2015.
* “Joint-range convexity for a pair of inhomogeneous quadratic functions with applications”, Plenary conference delivered in XII International Seminar on Optimization and Related Areas, Instituto de Matemática y Ciencias Afines (IMCA), Universidad Nacional de Ingeniería, Lima - Perú, 05-09 October, 2015.
* “Local optimality implies global for a class of nonconvex integrals - Convexity of the image for a pair of quadratic functions”, Invited speaker in Recent trends in differential equations: an international conference to celebrate the 75th birthday of Arrigo Cellina and 60th birthday of Alberto Bressan, Universidad de Aveiro, Departamento de Matemática Aplicada, Aveiro-Portugal, 27 - 29 June, 2016.
* “The standard quadratic optimization problem beyond the polyhedral case reveals hidden convexity”, Plenary Conference at VIII International Congress of Computational and Applied Mathematics, Facultad de Ciencias, Universidad Nacional de Ingeniería, Lima-Perú, August 23 - 26, 2016.
* “The conjugate of one-dimensional set-valued maps and related properties”, Invited speaker in Third International Conference on Set-Valued Variational Analysis and Set Optimization with Applications to Economics, Finance, Statistics and Game Theory, Vienna University of Economics and Business, Vienna - Austria, 19 - 23 September, 2016.
* “Convexity: can we avoid it?”, Plenary conference delivered in occasion of the XXX Jornadas de Matemática de la Zona Sur, Campus San Andrés, Universidad Católica de la Santísima Concepción, Concepción-Chile, April 26-28, 2017.
* “The standard quadratic optimization problem and its extensions: strong duality, hidden convexity and S-lemma”, Contributed talk at XII International Symposium on Generalized Convexity/Monotonicity, Hajdúszoboszló - Hungary, August 27-September 02, 2017.
* “Convexity behind strong duality for a class of nonconvex quadratic optimization problems”, Invited conference delivered in XIII International Seminar on Optimization and Related Areas, Instituto de Matemática y Ciencias Afines (IMCA), Universidad Nacional de Ingeniería, Lima - Perú, 09 - 13 October, 2017.
* “Nonconvex integrals in L 1 : strong duality, existence and local/global optimality”, Invited conference delivered in International Workshop on Optimization and Variational Analysis, Termas de Cauquenes, Universidad de O’higgins, Rancagua - Chile, 10 - 11 January, 2018.
* “A zero-scale asymptotic analysis for quasiconvex functions and related properties”, Contributed talk at International Conference on Variational Analysis and Nonsmooth Optimization, Martin-Luther Universität Halle-Wittenberg, Halle (Saale) - Germany, 28 June - 01 July, 2018.
* “Optimizando durante toda la vida”, Plenary conference delivered in occasion of the XXVII Congreso de Matemática Capricornio (COMCA), Campus Coloso, Universidad de Antofagasta, Antofagasta-Chile, July 25 - 27, 2018.
* “Quasiconvex optimization under zero-scale asymptotic analysis”, Contributed talk delivered in occasion of the XXVII Congreso de Matemática Capricornio (COMCA), Campus Coloso, Universidad de Antofagasta, Antofagasta-Chile, July 25 - 27, 2018.
* “The quadratic world and convexity with applications in nonconvex optimization”, Plenary Conference at IX International Congress of Computational and Applied Mathematics, Facultad de Ciencias, Universidad Nacional Agraria La Molina, Lima-Perú, August 06 - 09, 2019.
* “A new notion of asymptotic function in quasiconvex optimization with application to quadratic programming”, Contributed talk at Miniworkshop on “Optimización: herramientas teóricas y algoritmos” IX International Congress of Computational and Applied Mathematics, Facultad de Ciencias, Universidad Nacional Agraria La Molina, Lima-Perú, August 06 - 09, 2019.
* “A quadratic allocation process for a continuum of traders without standard convexity”, Invited conference delivered in XIV International Seminar on Optimization and Related Areas, Instituto de Matemática y Ciencias Afines (IMCA), Universidad Nacional de Ingeniería, Lima - Perú, 07 - 11 October, 2019.
* “Sums of quasimonotone operators and sums of quasiconvex functions via quasimonotone family”, Invited conference at Workshop on Optimization and Variational Analysis (honoring Terry Rockafellar’s 85th birthday), CMM, University of Chile, Santiago-Chile, January 20 - 21, 2020.
* “Optimización positivamente homogégenea: de la programación matemática a integrales no convexas”, Plenary conference at Evento Científico in occasion of 60 anniversary of Facultad de Ciencias (Universidad Nacional de Ingeniería), UNI - IMCA, Lima-Perú,September 22 - 24, 2020. (Virtual)
* “Optimización homogénea no convexa”, Plenary conference at XIV International Fast Workshop on Applied and Computational Mathematics, Universidad Nacional de Trujillo, Trujillo-Perú, January 07 - 08, 2021. (Virtual)

3. Member of (International) Scientific Committee/Program (2015 ->):
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• Main Organizer and Chairman of the Miniworkshop on “Optimización: herramientas teóricas y algoritmos” at IX International Congress of Computational and Applied Mathematics, (CIMAC IX) (August 06 - 09, 2019), Facultad de Ciencias, Universidad Nacional Agraria La Molina (UNALM), Lima-Perú.
• IX Congreso Internacional de Matemática Aplicada y Computacional (CIMAC IX) (August 06 - 09, 2019), Universidad Nacional Agraria La Molina (UNALM), Lima - Perú.
• XXVII Congreso de Matemática Capricornio (COMCA), (July 25 - 27, 2018), Campus Coloso, Universidad de Antofagasta, Antofagasta - Chile.
• XI Fast Workshop on Applied and Computational Mathematics (January 04 - 06, 2018), Universidad Nacional de Trujillo, Escuela de Postgrado, Departamento de Matemáticas, Trujillo - Perú.
• XII International Symposium of Generalized Convexity and Monotonicity (August 27 - September 02, 2017), Institute of Mathematics, University of Debrecen, Hajdúszoboszló - Hungary.
• XXX Jornadas de Matemática de la Zona Sur, Universidad Católica de la Santísima Concepción, Concepción-Chile, April 26 - 28, 2017.
• XIII International Seminar on Optimization and Related Areas, (October 09-13, 2017).
• XXX Jornadas de Matemática de la Zona Sur, (April 26-28, 2017), Universidad Católica de la Santísima Concepción, Concepción - Chile.
• X Fast Workshop on Applied and Computational Mathematics (January 06 - 07, 2017), Universidad Nacional de Trujillo, Departamento de Matemáticas, Trujillo - Perú.
• Third International Conference on Set-Valued Variational Analysis and Set Optimization with Applications to Economics, Finance, Statistics and Game Theory (16-19 September, 2016), Vienna University of Economics and Business, Vienna - Austria.
• VIII Congreso Internacional de Matemática Aplicada y Computacional (CIMAC VIII) (August 23 - 26, 2016), Universidad Nacional de Ingeniería, Facultad de Ciencias, Departamento de Matemáticas, Lima - Perú.
• IX Fast Workshop on Applied and Computational Mathematics (January 06 - 07, 2016), Universidad Nacional de Trujillo, Departamento de Matemáticas, Trujillo - Perú.
• Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO 2015) (May 11 - 13, 2015), Lorraine University, Metz - France.
• VII Congreso Internacional de Matemática Aplicada y Computacional (CIMAC VII)

4. International cooperation projects
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Fondecyt-Conicyt:
* Main researcher of the Project FONDECYT 1212004 (ANID-Chile): “Further developments in mathematical optimization and quasimonotone operators”, April 2021 - March 2024.
* Main researcher of the Project FONDECYT 1181316 (ANID-Chile): “From mathematical programming to calculus of variations without standard convexity”, April 2018 - March 2021.
* Main researcher of the Project FONDECYT 115-0973 (CONICYT-Chile): “Optimization theory and mathematical programming without standard convexity”, March 2015 - February 2018.
* Main researcher of the Project FONDECYT 112-0980 (CONICYT-Chile): “Further developments in nonconvex optimization and equilibria”, March 2012 - February 2015.
* Main researcher of the Project FONDECYT 110-0667 (CONICYT-Chile): “Unifying general vector optimization problems and optimality conditions”, March 2010 - February 2012.
* Main researcher of the Project FONDECYT 107-0689 (CONICYT-Chile): “Further development in multivalued complementarity problems and vector optimization”, March 2007- February 2010.
* Main researcher of the Project FONDECYT 706-0106 (International Co-operation) (CONICYT-Chile): “Non-convex vector optimization and mathematical programming: existence and optimality conditions”, March 2006 - February 2007.
* Main researcher of the Project FONDECYT 104-0610 (CONICYT-Chile): “Non-convex vector optimization and mathematical programming: existence and optimality conditions”, March 2004 - February 2007.
* Main researcher of the Project FONDECYT 101-0116 (CONICYT-Chile): “Further developments in convex/non-convex optimization theory”, March 2001 - February 2004.
* Main researcher of the Project FONDECYT 199-0348 (CONICYT-Chile): “Nonclassical problems in optimization theory and Calculus of variations”, March 1999 - February 2001.
* Main researcher of the Project FONDECYT 197-0931 (CONICYT-Chile): “Further developments in the Calculus of Variations and Optimization Theory”, March 1997 - February 1999.
* Main researcher of the Project FONDECYT 195-1148 (CONICYT-Chile): “Some problems in Optimization in the absence of the Convexity/Superlinearity condition”, March 1995 - February 1997.

Fondap-Basal-Conicyt:
* Associate Researcher of the Basal Proyect FB210005 (ANID-Chile), ``Optimization and Equilibria'', Centro de Modelamiento Matemático (CMM), Universidad de Chile, November 2021 - December 2026.
* Associate Researcher of Proyecto Apoyo a Centro de Excelencia ACE210010 (ANID-Chile), Centro de Modelamiento Matemático (CMM), Universidad de Chile, October 2021 - April 2022.
* Associate Researcher of the Basal Project (CONICYT-Chile) AFB170001, “Optimization and Equilibria”, CMM, Universidad de Chile, May 2008 - April 2021.
* Researcher of the Project FONDAP-Matemáticas Aplicadas II (CONICYT), May 2000 - December 2010: “Optimization and Equilibria”.
* Researcher of the Project FONDAP (CONICYT), May 1997 - December 1999: “Optimization” being responsible of the sub-project “Non-classical variational problems”.

Programa Regional MATH-AmSud-CONICYT:
* MATH-AmSud, 22-MATH-07(AMSUD220020) Researcher “Optimality conditions and proximal methods for generalized convex optimization problems”. 01 January 2023 - 31 December 2024.
* MATH-AmSud 17math-06: Coordinator of the Chilean team and Researcher “From monotonocity to dynamic and equilibrium: structures and applications”. 01 January 2017 - 31 December 2018.
* MATH-AmSud 13math-01: Researcher “Variational analysis and its aplications to optimization, monotone operators, convex analysis and Nash equilibrium problems”. 01 January 2013 - 31 December 2014.

Ecos-Conicyt:
* Researcher of the Project ECOS-CONICYT (2010-033), January 2011 - December 2013. “Optimización no Diferenciable y Análisis Variacional: Teoría y Aplicaciones.
* Researcher of the Project ECOS-CONICYT, January 1997 - December 1999:“Optimisation et Analyse non-linéaire” being responsible of the sub-project“Problèmes d’existence en calcul des variations”.