Noticias en español
Critical angles between two convex cones
In this talk we present a general theory of critical angles for a pair of closed convex cones via the optimization point of view. The angular analysis for a pair of specially structured cones will be also discussed. For instance, we work with linear subspaces, polyhedral cones, revolution cones, topheavy cones and cones of matrices. This is a joint work with Alberto Seeger.
Read MoreModeling, Simulation and Optimization of a Polluted Water Pumping Process in Open Sea
Abstract: Oil spill contamination in open sea has provoked some of the major environmental disaster in history. The ecological and economic impacts of such hazards are generally important and should be controlled as quickly as possible. One of the major cleaning techniques for these hazards is the use of skimmer ships. Those ships use various pumps distributed along the vessel perimeter to suck the oil from the surface of the water directly into storage units. In this work, we are interested in improving this process. To do so, we first introduce a mathematical model to simulate the...
Read MoreThe usefulness of calmness in optimization
Abstract: The aim of this talk is to present the role that plays the calmness property in optimization, namely for the existence of KKT multipliers, subdifferential calculus, ….. A collection of sufficient conditions ensuring this property will be presented.
Read MoreChance-constrained problems and rare events: an importance sampling approach.
Abstract: We study chance-constrained problems in which the constraints involve the probability of a rare event. We discuss the relevance of such problems and show that the existing sampling-based algorithms cannot be applied directly in this case, since they require an impractical number of samples to yield reasonable solutions. Using a Sample Average Approximation (SAA) approach combined with importance sampling (IS) techniques, we show how variance can be reduced uniformly over a suitable approximation of the feasibility set, and as a result the problem can be solved with much fewer...
Read MoreThe dynamics of optimal transportation
Given a cost function and two probability measures on a compact manifold, the Monge problem is concerned with the study of minimizers of a transportation cost among transport maps between these two measures while the Kantorovitch problem is concerned with optimal transport plans. We will explain the main difference between these two optimization problems. Then we will address the uniqueness of optimal transport plans for the Kantorovitch problem. We will show that the uniqueness issue is related with the properties of some dynamics associted to the...
Read MoreSlope and Geometry in Variational Mathematics
Abstract: Various notions of the “slope” of a real-valued function pervade optimization and variational mathematics more broadly. In the semi-algebraic setting—an appealing model for concrete variational problems — the slope is particularly well-behaved. This talk sketches a variety of surprising applications, illustrating the unifying power of slope. Highlights include error bounds for level sets, the existence and regularity of steepest descent curves in complete metric spaces (following Ambrosio et al.), transversality and the convergence of von Neumann’s alternating projection...
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