David Salas Videla ● Profesor Asistente

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""]TRANSFERENCIA SUPERCOMPUTACIÓN PARA INNOVACIÓN EN SALUD REGIONAL: HPC-UOH Y HRLBO[/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""]El monto corresponde a 23500 EUR con tasa de conversión de 1022,47 CLP/EUR. Este es el presupuesto asignado para el primer año.[/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""]Chile, Peru and France, as well as many countries in South America and Europe, share a very similar systems to deal with their electricity markets. In parallel, all three countries (together with the rest of the world) are being affected by climate change in many aspects, such as scarcity of water, intense droughts, pollution and the greenhouse effect, the necessity of new energy sources, just to name a few. To face these challenges, we need new technology coming from many fields of science. One of such fields is mathematics and in particular, stochastic optimization and game theory. These theoretical fields allow us to model economic interactions, management solutions, optimal design and operations, among many other relevant aspects of Natural Resources and Energy Management. In the present project, we propose to develop new theoretical and numerical advances in four research lines, concerning Stochastic Optimization and Game Theory. Namely, we will work on: 1) Continuity-like properties in Equilibrium problems; 2) Regularity in Generalized Equilibrium problems; 3) Bilevel games with decision-dependent uncertainty; and 4) Algorithms and mechanism design in learning games. The four research lines are strongly motivated by the aforementioned applications.[/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""]Estudio de problemas de optimización y juegos con incertidumbre dependiente de decisiones. Estudio a nivel teórico y algorítmico. Estudio de aplicaciones.[/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""]El Centro de Modelamiento Matemático (CMM) es un centro científico líder en Chile para la investigación y aplicaciones de las matemáticas. Fue inaugurado en abril del 2000 y forma parte de la Facultad de Ciencias Físicas y Matemáticas (FCFM) de la Universidad de Chile, en la que se encuentra la principal y más antigua escuela de ingeniería del país. Su objetivo es crear nuevas matemáticas y utilizarlas para resolver problemas provenientes de otras ciencias, la industria y las políticas públicas.[/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""]En este proyecto, se busca general nuevas tecnologías que permitan mejorar el manejo de recursos hídricos en la sexta región. Director de línea "Gestión de Riego Intrapredial con Inteligencia Artificial"[/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""]Stochasticity in optimization and game theory is a very important aspect to model more accurately real-world problems in many different areas (see for instance [6]). In optimization problems as well as in one-level games, namely, Nash equilibrium problems, stochasticity aspects have received quite a lot of attention for a while and have also been well studied [22]. However, for the branch of bilevel games quite few studies have included in their analysis stochastic aspects in their models. A bilevel game is basically to split a finite set of players into two levels: the leaders or upper-level players, and the followers or lower-level players. In the model, the followers react in a passive way to the leaders' actions, while the leaders compete in the upper level trying to actively anticipate the followers' reaction. Moreover, in each level, the interaction is non-cooperative as in Nash equilibrium problems. Bilevel games have been recognized as one of the most complex and at the same time very useful models in the literature [17]. Bilevel games, and more precisely the problem of the leaders in a bilevel game, face an ambiguity/uncertainty whenever the followers' reaction is not necessarily uniquely determined for each leaders' decision. To deal with this ambiguity two main approaches are well-known the optimistic and the pessimistic. The weakness of these two approaches is that both are quite extreme and the optimistic one lacks of real modeling foundations, putting the leaders in a quite naive position. Recently, in [9] a general stochastic approach has been proposed to solve this ambiguity, which is seen as an uncertainty of the problem, providing also a specific approach that seems to be more reasonable than the optimistic one, from a modeling point of view. The stochasticity in the stochastic approach is an endogenous one since it corresponds to a decision-dependent uncertainty [1, 23]. But, of course, stochasticity might also come from an exogenous side, that is, when some of the parameters defining the game, such as future demand and prices, 1 forecasts of winds and clouds, are uncertain and possibly follow some probability distribution. This has been considered in [34, 12, 13, 16]. In the second part of the project, which is the applied part, we are interested in using the developed theoretical framework of bilevel games with stochastic aspects to a problem of contaminated water resource management, which has high levels of stochasticity. The scarcity of water resource and its efficient use has been recognized as an extremely important problem in Chile and the whole world, for agricultural, industrial, and human use. Moreover, after any use, there is an outflow of water which has generally more contaminants than the inflow. Depending on the type and quantity of contaminants the outflow of water could be reused, but sometimes giving less profit to the entity. The general situation is full of uncertainties, since the entities do not share their information. Moreover, the main source of information for us will be measurements on the quality of water at different strategic points and punctual events of contamination registered by inspection, which is simply a qualitative data. Therefore, we propose first to apply predictive models and machine learning to do inverse engineering in order to understand the game played by the different actors. Then we want to study the underlying one-level game and study the design of mechanisms (bilevel game) so that we can move the equilibrium to a desired goal. In a somehow similar spirit, in [30, 31, 10] game theory techniques have been used to analyze the behavior of companies sharing contaminated water in the context of eco-industrial parks, while in [36] also a bilevel model is used for a water resource optimal allocation problem.[/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""][/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]

[vc_section el_class="container mx-auto align-items-center circle--pattern" css=".vc_custom_1648956589196{padding-top: 3rem !important;}"][vc_row el_class="pb-5"][vc_column][vc_wp_custommenu nav_menu="6"][uoh_breadcrumb_component automatic_breadcrumb="true"][uoh_title_component title_dropdown="big" title_decorator="true"]{{title}}[/uoh_title_component][vc_column_text css=""]Nonsmooth dynamical system involving regular structures[/vc_column_text][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649209804184{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5"][vc_row el_class="container mx-auto align-items-center p-md-0 pt-5"][vc_column el_class="p-0"][/vc_column][/vc_row][/vc_section][vc_section css=".vc_custom_1649210787516{background-color: #f6faff !important;}" el_class="p-md-0 pt-md-5 pb-md-5"][vc_row el_class="container mx-auto align-items-center"][vc_column][/vc_column][/vc_row][/vc_section]