Contributions

Contributions at International Meetings

  • "Radially Symmetric Solutions for a Class of Non-convex Problems in the Calculus of Variations", presented at 1st European Conference on Elliptic and Parabolic Problems Pont-[â]-Mousson France, June 17-21, 1991.

  • "Radial Solutions for some Classesof Non-convex Problems in the Calculus of Variations", presented at International Conference of Differential Equations EQUADIFF'91, Barcelona-Spain, August 26-31, 1991.

  • "The Lack of Lower Semicontinuity in the Calculus of Variations", presented at First Chilean-CEE School on Optimization and Third Franco-Latinoamerican Conference in Applied Mathematics, Santiago-Chile, August 1992.

  • "Applications of a duality theory in non-convex optimization", invited conference at Seminario en Optimización Matemática, Universidad Nacional de Ingeniería, Lima-Perú, July 5-9, 1993.

  • "Duality in non-convex optimization"(in Spanish), invited minicourse (a serie of three lectures) delivered in occasion of the III Congreso de Matemática Capricornio (COMCA), Antofagasta-Chile, August 4-7, 1993.

  • "El rol cd la convexidad en la elasticidad finita", Invited Conference delivered in occasion of the VII Coloquio Peruano de Física Matemática, Lima-Perú, August 1993.
  • "A constructive method for selections from the subdifferential of a convex function" (In Spanish), invited conference delivered in occasion of the IV Encuentro de Matemáticas y sus Aplicaciones, Facultad de Ciencias, Escuela Politécnica Nacional (EPN), Quito-Ecuador, July 04-08, 1994.

  • "C1-selections from the subdifferential of a convex function", presented at International Congress of Mathematicians, E.T.H. Zürich-Swizerland, August 3-11, 1994.

  • "Existence and non-existence in the Calculus of Variations" (In Spanish), Plenary conference delivered in occasion of the LXVI Encuentro Nacional de la Sociedad de Matemática de Chile, Valparaíso-Chile, October 28-29, 1994.

  • "An Introduction to the Calculus of Variations" (In Spanish), invited minicourse (a serie of three lectures) delivered in occasion of the IX Jornadas de Matemática de la Zona Sur, Chillán-Chile, April 26-28, 1995.

  • "Some Non-convex symmetric problems in the Calculus of Variations", invited conference delivered at 2do. Seminario en Matematica Aplicada y Optimización, Facultad de Ciencias, Universidad Nacional de Ingeniería, Lima-Perú, October 02-05, 1995.

  • "Subdifferentiability with respect to the continuous functions", invited conference delivered at 2das. Jornadas Catalanas de Matemática Aplicada, Four Solaire, Font Romeu-Odeillo, France, November 29 - December 01, 1995.

  • "Simplified Global Optimality Conditions for Differences of Phi-convex Functions"(with J.E. Martinez-Legaz), Conference delivered at V Symposium on Generalized Convexity and its Applications, CIRM-Luminy, Marseille-France, June 17-21, 1996.

  • "Some remarks on the Ekeland variational principle" (In Spanish), invited conference delivered in occasion of the V Encuentro de Matemáticas y sus Aplicaciones, Facultad de Ciencias, Escuela Politécnica Nacional (EPN), Quito-Ecuador, July 22-26, 1996.

  • "Una Introducción al Cálculo de Variaciones y aplicaciones en Elasticidad Finita", invited minicourse (a serie of three lectures) delivered in occasion of the Seminario Nacional de Aplicaciones de la Matemática, Facultad de Ciencias Naturales y Formales, Universidad Nacional de San Agustín, Arequipa-Perú, October 14-18, 1996.

  • "An attempt to define the conjugate of set-valued maps and related properties", invited talk delivered within the cluster session (also Chairman) Generalized convexity at XVI International Symposium on Mathematical Programming, EPFL, Lausanne-Switzerland, August 24-29, 1997.

  • "Minimizing integral functionals via Lyapunov-type theorems", invited minicourse (a serie of three lectures) delivered at 3er. Seminario Internacional en Matematica Aplicada y Optimización, Facultad de Ciencias, Universidad Nacional de Ingeniería, Lima-Perú, October 06-10, 1997.

  • "Un resultado del tipo Lyapunov en Cálculo de Variaciones" (with V. Briceño), talk delivered in occasion of the LXIX Encuentro Nacional de la Sociedad de Matemática de Chile, Olmué-Chile, October 24-25, 1997.

  • "A variational problem in Mathematical Economics", invited conference delivered in occasion of the Inauguration of the Instituto de Matemática y Ciencias Afines (IMCA), Universidad Nacional de Ingeniería, Lima-Perú, December 08-12, 1997.

  • "Optimal solutions to some variational problems in Consumer theory" (In Spanish), invited conference delivered in occasion of the VI Encuentro de Matemáticas y sus Aplicaciones y Cuarta Escuela Andina de Ecuaciones Diferenciales, Facultad de Ciencias, Escuela Politécnica Nacional (EPN), Quito-Ecuador, July 06-10, 1998.

  • "Optimal solutions to some variational problems arising in Economics", presented at International Congress of Mathematicians, T.U. Berlin, Berlin-Germany, August 18-27, 1998.

  • "Optimal planning to variational problems arising in Economics", invited conference delivered in occasion of the 5ème Congrés Franco-Latinoaméricain de Mathématiques Appliquées, Universidad de Chile, Departamento de Ingeniería Matemática, Santiago-Chile, December 15-18, 1998.

  • Chairman of the special session "Optimization and Calculus of Variations" and invited conference "Pseudomonotone equilibrium problems and calculus of variations" delivered in occasion of the IX Congreso de Matemática Capricornio (COMCA), Antofagasta-Chile, August 04-07, 1999.

  • "Simplified optimality conditions for a difference of vector-valued functions", presented at (also Chairman) VI International Symposium on Generalized Convexity/Monotonicity, Karlovassi, Samos-Greece, August 30-September 3, 1999.

  • "Noncoercive generalized equilibrium problems: the quasiconvex case", invited conference delivered at 4to. Seminario Internacional en Matematica Aplicada y Optimización, Facultad de Ciencias, Universidad Nacional de Ingeniería, Lima-Perú, October 04-08, 1999.

  • "The conjugate of set-valued maps and related properties", (jointly with W. Oettli) invited conference delivered at 4to. Seminario Internacional en Matematica Aplicada y Optimización, Facultad de Ciencias, Universidad Nacional de Ingeniería, Lima-Perú, October 04-08, 1999.

  • "Non-coercive vector equilibrium problems: existence of solutions", presented at French-German-Italian Conference on Optimization, Université Montpellier II, Montpellier-France, September 04-08, 2000.

  • "A unified approach in optimization theory" (In Spanish), Invited conference delivered in occasion of the LXXII Encuentro Nacional de la Sociedad de Matemática de Chile, Punta de Tralca-Chile, October 26-28, 2000.

  • "The equilibrium problems and variational problems ", invited lectures (two) delivered at the Summer School, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción-Chile, January 08-19, 2001.

  • "Two variational problems in consumption theory" (In Spanish), invited talk delivered in occasion of the XV Jornadas de Matemática de la Zona Sur, Concepción-Chile, April 26-28, 2001.

  • "Existence in convex vector optimization problems and optimality conditions in non-convex set-valued minimization" contribuited lecture at XXXIV Workshop on Optimization and Control with Applications, Erice-Italy, July 09-17, 2001.

  • "A unifying approach in optimization theory and applications", invited lecture delivered at Tenth International Colloquium on Numerical Analysis and Computer Science with Applications, Plovdiv-Bulgaria, August 12-17, 2001.

  • "Variational problems in mathematical economics ", Plenary Conference delivered at XIX Coloquio Nacional de Matemática, Universidad Nacional de Trujillo, Trujillo-Perú, November 05-10, 2001.

  • "Existence theory for finite dimensional equilibrium problems", invited mini-course (two lectures) delivered at XIX Coloquio Nacional de Matemática, Universidad Nacional de Trujillo, Trujillo-Perú, November 05-10, 2001.

  • "Radial epiderivatives and recession function in non-convex vector optimization", invited talk delivered in occasion of the 6éme Congrés Franco-Latinoaméricain de Mathématiques Appliquées, Universidad de Chile, Center for Mathematical Modeling, Santiago-Chile, December 17-21, 2001.

  • "Vector optimization problems: existence of solutions and optimality conditions", Plenary Conference delivered in occasion of the XVI Jornadas de Matemática de la Zona Sur, Universidad Católica del Maule, Talca-Chile, April 26-28, 2002.

  • "Characterizations of the existence of solutions for a class of non-convex vector optimization problems", invited lecture delivered in the International Conference on Optimization and Optimal Control, Mongolian State University and Center of Science and Culture of the Mongolian Academy of Sciences, Ulaanbaatar-Mongolia, August 13-17, 2002.

  • "Characterizations of the non-emptiness/compactness of the solution set to equilibrium problems", presented at International Congress of Mathematicians, Beijing International Convention Center, Beijing-China, August 20-28, 2002.

  • "On a class of non-convex vector optimization problems", invited lecture delivered at International Symposium of Mathematics within the Special Sesion on Optimization and Calculus of Variations, Universidad de Magallanes, Punta Arenas-Chile, November 12-15, 2002.

  • (with D. Carrasco) "Representation of E-subdifferential for a class of non-convex/convex functions", invited lecture delivered at International Symposium of Mathematics within the Special Sesion on Optimization and Calculus of Variations, Universidad de Magallanes, Punta Arenas-Chile, November 12-15, 2002.

  • "Radial epiderivatives and optimality conditions in non-convex scalar/vector optimization", invited plenary conference delivered at 6to. Seminario Internacional en Matemática Aplicada y Optimización, Instituto de Matemática y Ciencias Afines (IMCA), Universidad Nacional de Ingeniería, Lima-Perú, October 06-10, 2003.

  • "On a non-convex variational problem of the Laplacian", talk delivered in occasion of the LXXV Encuentro Nacional de la Sociedad de Matemática de Chile within the Special Sesion Optimization, Vicuña-Chile, 30-31 October and 1st November, 2003.

  • (with C. Vera) "An optimal 2D alternative theorem and nonconvex optimization problems", presented at V Brazilian Workshop on continuous optimization, Florianópolis - Brazil, March 22-25, 2004.

  • (with R. Lóopez) "Asymptotic analysis, existence and sensitivity results for linear complementary problems", presented at 12th French-German-Spanish Conference on Optimization, Universite de Avignon, Avignon - France, September 20-24, 2004.

  • (with C. Vera)"Computing the weakly Pareto minima for bicriteria quasiconvex mappings on the real-line without derivative", talk delivered at LXXVI Encuentro Nacional de la Sociedad de Matem�ica de Chile within the Special Sesion Optimization, Olmué-Chile, October 28 - 30, 2004.

  • "A basic theory of multivalued complementarity problems", plenary conference atV Italian-Latin American Conference on Apllied and Industrial Mathematics (ITLA 2004) , Universidad Nacional de Trujillo, Trujillo - Perú, December 15-18, 2004.

  • "Is it really a drawback the convexity in optimization?", presented at 6eme Congres Franco-Latinoamericain de Mathematiques Appliquees, Universidad de Chile, Center for Mathematical Modelling, Santiago - Chile, January 14-18, 2005.

  • "Weak efficiency in convex and quasiconvex vector minimization without scalarizing", plenary conference at 7mo. Seminario internacional en Matematica Aplicada y Optimizacion, Instituto de Matematica y Ciencias Afines (IMCA), Universidad Nacional de Ingenieria, Lima-Perú, October 03-07, 2005  

  • "Weak efficiency in multiobjective quasiconvex minimization", plenary conference at III  Congreso Internacional de Matematica Aplicada y Computacional (CIMACIII), Universidad Nacional del Callao,  Facultad de Ciencias Naturales y Matematica, Callao-Perú, January 30 - February 04, 2006.

  • "Asymptotic analysis for equilibrium and multivalued complementarity problems beyond copos- itivity and positive homogeneity", contributed lecture delivered at VIEW´s on Differential Equations (VIEW´s 2006), Universidad de Aveiro, Departamento de Matemática Aplicada, Aveiro-Portugal, 21 - 24 June, 2006.

  • "Asymptotically bounded multifunctions and the MCP beyond copositivity and positive homogeneity", presented at International Congress of Mathematicians (ICM2006), Palacio Municipal de Congresos, Madrid-Spain, August 22-30, 2006.

  • "Asymptotically bounded multifunctions and the multivalued complementarity problem", Invited conference delivered in occasion of the Inauguration of the Building of the Instituto de Matemática y Ciencias Afines (IMCA), Universidad Nacional de Ingeniería Lima-Perú, December 04-09, 2006.

  • "Weak efficiency in convex and quasiconvex vector optimization problems", invited talk within the Stream session \Vector and Set-valued Optimization" at 22nd European Conference on Operational Research (EURO XXII 2007), University of Economics, Prague-Czech Republic, 08 - 11 July, 2007.

  • "Characterizing efficiency without linear structure", invited conference delivered in 7mo. Seminario Internacional en Matematica Aplicada y Optimización, Instituto de Matemática y Ciencias Afines (IMCA), Universidad Nacional de Ingeniería, Lima-Perú, 01-05 October, 2007.

  • Multivalued complementarity problems with asymptotically bounded multifunctions", invited talk at VI Journees Franco-Chiliennes d'Optimisation, Universite Sud Toulon-Var, Toulon-France, May 19-21, 2008.

  • An optimal alternative theorem and quasiconvex multiobjective optimization", Plenary Conference at XI Encuentro de Matemática y sus Aplicaciones, Escuela Politécnica Nacional, Quito- Ecuador, July 07-11, 2008.

  • Overview on generalized convexity and vector optimzation", Lecturer of two sessions at (also Chairman) 2nd Summer School on Generalized Convex Analysis: Introduction to Theory and Applications, Department of Applied Mathematics, National Sun Yat-sen University, Kaoshiung-Taiwan, July 15-19, 2008.

  • Asymptotically bounded multivalued complementarity problems", Contributed talk at (also Chairman) IX International Symposium on Generalized Convexity/Monotonicity, Department of Applied Mathematics, National Sun Yat-sen University, Kaoshiung-Taiwan, July 21-25, 2008.

  • Convexity behind the non-convexity in optimization", Plenary Conference at IV Interna- tional Congress of Computational and Applied Mathematics, Facultad de Ciencias Físicas y Matemáticas, Universidad Nacional Pedro Ruiz Gallo, Lambayeque-Perú, September 15-19, 2008.

  • Convexity behind the nonconvexity in Optimization", invited talk at Workshop on Variational Analysis, Departamento de Ingeniería Matemática - CMM, Universidad de Chile, Santiago- Chile, November 10-13, 2008.

  • Scalarizing and unifying (approximate) efficiency: a basic theory and optimality conditions, Keynote Speaker at The 2nd International Conference of Nonlinear Analysis and Optimization (NAOP 2009), Departament of Mathemtics, University of Isfahan, Isfahan-Iran, May 13-15, 2009.

  • Hidden convexity in nonconvex optimization, Invited Conference at VI Italian-Latin American Conference on Applied and Industrial Mathematics (ITLA 2009), (14-18 September, 2009), Escuela Politecnica Nacional (EPN), Quito, Ecuador.

  • Unifying vector optimization problems: a theorical approach and optimality conditions, invited conference delivered in IX Seminario Internacional en Matemática Aplicada y Optimización, Instituto de Matemáticas y Ciencias Afines (IMCA), Universidad Nacional de Ingeniería, Lima-Perú, 05-09 October 2009.

  • Are we really far from convexity in nonconvex optimization?, invited speaker delivered in International Conference on Optimization and Its Applications, Departament of Mathematics, Banaras Hindu University (BHU), Varanasi - India, 16-18 February, 2010.

  • A unification of (approximate) vector optimization problems: complete scalarizations and optimaly conditions, invited talk delivered in 24th Mini EURO Conference on Continuous Optimization and Information-Based Technologies in the Financial Sector, MEC-EurOPT-2010, Izmir University of Economics, Izmir - Turkey, 23 - 26 June, 2010.

  • Charaterizing the Lagrangian strong duality in constrained nonconvex optimization, presented at International Congress of Mathematicians (ICM2010), Hyderabad International Convention Center (HICC), Hyderebad - India, 19 - 27 August, 2010.

  • Convexity is not far from non-convexity in optimization, invited talk at Arrigo Cellina´s 70th birthday, Nonlinear differential equations and control, Dipartimento de Matematica e Applicazioni, Universita di Milano-Bicocca, Milano-Italy, September 22-23, 2011.

  • Strong duality in cone-constrained nonconvex optimization with applications to non- convex variational problems, invited plenary session at International conference, Op- timization, Theory, Algorithms and Applications in Economics, A tribute to Juan En- rique Martinez-Legaz on his 60th birthday, Centre de Recerca Matematica (CRM), Barcelona-Spain, October 24-28, 2011.

  • "Existence and strong duality for a class of non-convex variational problems", Invited talk at IX Americas Conference on Differential Equations, Universidad Nacional de Trujillo, Trujillo - Perú, January 09-14, 2012

  • "Existence and strong duality for a class of nonconvex variational problems", Invited talk at Stream Session on Optimization and Calculus of Variations XXV Jornadas de Matemática de la Zona Sur, Concepción-Chile, April 18-20, 2012

  • "Scalarizing vector optimization problems with non-necessarily transitive preferences or solid cones" Invited talk and also chairman at International Mini-Conference on Set-Valued Variational Analysis and Optimization with Applications in Finance, Leucorea, Lutherstadt Wittenberg - Germany, August 16-19, 2012

  • "Efficiency and ordering variational principles", Invited talk delivered within the cluster session Muti-objective optimization at XXI International Symposium on Mathematical Programming, BTU, Berlin-Germany, August 19-24, 2012

  • "Characterization of efficiency via scalarization with ordering sets without solidness" within the Sesion "Efficiency and vector optimization with applications" at 26nd European Conference on Operational Research (EURO XXVI 2013), University La Sapienza Tor Vergata, Rome-Italy, 01 - 04 July, 2013.

  • "Characterizing strong duality in nonconvex (quadratic) programming", invited conference delivered at XI International Seminar on Optimization and Related Areas, Instituto de Matem´tica y Ciencias Afines (IMCA), Universidad Nacional de Ingeniería, Lima - Perú, 07-11 October, 2013

  • "Characterizing FJ and KKT points in nonconvex optimization with applications to a class of MPEC's", invited conference delivered at 2nd International Conference on Variational Analysis and Optimization, CMM, Universidad de Chile, Santiago - Chile, 07-10 January, 2014.

  • "Does convexity arise in optimization naturally?", invited conference delivered at Workshop about variational inequalities, equilibria and neighbouring problems, Dipartimento di Informatica, Università di Pisa, Italy, 29-30 May, 2014

  • "Convexity of the value function for a class of nonconvex variational problems: existence and optimality conditions" invited conference delivered at IV LatinAmerican Workshop on Optimization and Control, IMCA-UP, Lima, Perú, 15-18 July, 2014.

  • "Hidden convexity in nonconvex optimization",Contributed talk at XI International Symposium on Generalized Convexity/Monotonicity, IMPA, Rio de Janeiro-Brazil, August 25-30, 2014.

  • "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 flobal 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 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.

  • "Convexity behind strong duality for a class of nonconvex quadratic optimization problems", Plenary 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 L1 : 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 Universiät 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 6 - 9, 2019

  • "A new notion of symtotic function in quasiconvex optimization with applications to quadratic programming", Contributed talk, at Miniworkshop on "Optimización: herramientas teóricas y algortimos" IX International Congress of Computational and Applied Mathematics, Facultad de Ciencias Universidad Nacional Agraria La Molina, Lima-Perú, August 6 - 9, 2019.

  • "Simultaneous diagonalization under weak regularity and a characterization", Invited conference delivery in XIV International Seminar on Optimization and Related Areas, Instituto de Matemática y Ciencias Afines (IMCA), Universidad Nacional de Ingeniería, Lima - Perú, 7 - 11 October, 2019.