## Completely mixed linear games and irreducibility concepts for Z-transformations over self-dual cones.

Abstract: In the setting of a self-dual cone in a finite-dimensional real inner product space (in particular, over a symmetric cone in an Euclidean Jordan algebra), we consider zero-sum linear games. Motivated by dynamical systems, we concentrate on $Z$-transformations (which are generalizations of $Z$-matrices). It is known that a $Z$-transformation with positive (game) value is completely mixed (thus yielding uniqueness of optimal strategies). The present talk deals with the case of value zero. Motivated by the matrix-game result that a $Z$-matrix with value zero is completely...

Read More## All convex bodies in the subdifferential of a locally Lipschitz function.

Abstract: We construct a differentiable locally Lipschitz function f in R^d with the following property: for every convex body K of R^d, there exists x in R^d such that the subdifferential of f at x coincides with K (in the sense of limiting or Clarke). We show that our technique can be further refined to recover all compact connected subsets with nonempty interior in the image of the limiting subdifferential of a locally Lipschitz function. We end this talk with a brief discussion about how large the set of functions with the aforementioned property is.

Read More## Copositive and Linear Conic Optimization Revisited via Linear Semi-Infinite Optimization.

Abstract: In this talk we show existence, optimization and duality theorems for copositive and linear conic optimization problems. These results are obtained from the semi-infinite linear optimization theory, which has been previously updated in two articles in collaboration with Andrea Ridolfi and Virginia Vera de Serio.

Read More## Desarrollo de un colector de concentración solar Fresnel para calor de procesos en Ecuador.

Abstract:El grupo de investigación SCINERGY de la Escuela Politécnica Nacional ha emprendido en la investigación y desarrollo de un colector solar de concentración tipo Fresnel para producción de calor de procesos (< 180ºC), que pueda ser construido con las capacidades tecnológicas locales. Este trabajo muestra los avances y los retos alrededor de este objetivo. El desarrollo local de esta tecnología apoyaría en la diversificación de la matriz energética introduciendo fuentes renovables.

Read More## An SDE perspective on stochastic convex optimization.

Abstract: We analyze the global and local behavior of gradient-like flows under stochastic errors towards the aim of solving convex optimization problems with noisy gradient input. We first study the unconstrained differentiable convex case, using a stochastic differential equation where the drift term is minus the gradient of the objective function and the diffusion term is either bounded or square-integrable. In this context, under Lipschitz continuity of the gradient, our first main result shows almost sure weak convergence of the trajectory process towards a minimizer of the objective...

Read More## Analysing necessary optimality conditions for a time optimal control problem in Wasserstein spaces.

Abstract: We are interested in developing necessary optimality conditions in the form of a Pontryagin maximum principle for the minimal time Bolza optimal control problem with constraints in the final time. In this problem, the dynamic is given by a non-local continuity equation in the Wasserstein space of probability measures, the set of controls are taken in open-loop form and the set of constraints is represented by functional inequalities applied to the terminal time. To this end, we relate the main challenges of this problem from which a fair amount is accounted by the fact that...

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