Noticias en español
Variable stepsize splitting methods as relocated fixed-point iterations.
Abstract: Splitting methods exploit model structures to decompose complex optimisation problems into simpler pieces, easier to handle. A prominent instance in this family is the Douglas-Rachford algorithm, which stands out due to its simplicity and numerical stability. Traditional convergence guarantees assume constant stepsizes, while the theory with variable stepsizes is scarce, limiting the improvement of numerical performance. Including the aforementioned method, several optimisation algorithms can be recast as fixed-point iterations using constant parameters, and thus share the same...
Read MoreConvergence Rates for Stochastic Proximal and Projection Estimators
Abstract: In this talk, we discuss explicit convergence rates for the stochastic smooth ap-proximations of infimal convolutions introduced and developed in [2, 3]. In particular,we quantify the convergence of the associated barycentric estimators toward prox-imal mappings and metric projections. We prove a dimension-explicit √δ bound, with explicit constants for the proximal mapping, in the ρ-weakly convex (possibly nonsmooth) setting, and we also obtain a dimension-explicit √δ rate for the metric projection onto an arbitrary convex set with nonempty interior. Under additional regularity,...
Read MoreOptimización del diseño minero considerando la sustentabilidad de la operación
Abstract: El diseño de una operación minera es una decisión estratégica que define la geometría de la explotación, condicionando el acceso al mineral, los costos e inversiones necesarios para esto. El diseño define el método de extracción, el manejo de materiales y por lo tanto los equipos. Más aún, el diseño minero incluye la infraestructura dentro y fuera de la mina, incluyendo plantas tratamiento, botaderos y relaves. Dada esta relevancia, son múltiples los esfuerzos que se han realizado para encontrar un diseño óptimo. Sin embargo, a pesar de los avances en modelos y algoritmos para...
Read MoreOptimal Control of Sweeping Processes: Addressing the Challenge of Mixed Constraint.
Abstract: In the quest to model elastoplastic mechanical systems, J.J. Moreau introduced the concept of a ‘sweeping process’ in the 1970s. These systems are characterized by their dynamics, described by a discontinuous differential inclusion that can be expressed in terms of a cone, posing a unique challenge. This presentation delves into the complexities of establishing necessary optimality conditions for optimal control problems involving such dynamics, particularly when subject to mixed constraints on state and control variables. We will explore two distinct approaches to...
Read MoreNonlinear Reach Controllability in Two-Dimensional Simplices.
Abstract: This talk addresses the problem of constrained reach controllability in two dimensions. Considering a nonlinear controlled dynamics (given by an ODE) within a two-dimensional simplex, the goal is to design a feedback control—either continuous or piecewise continuous—that can steer any point inside the simplex to the outside, subject to the additional restriction that exit is only allowed through one of its faces. We will present sufficient conditions to determine whether a given control constitutes a solution, as well as a result ensuring the existence of solutions for affine...
Read MoreBilevel Hyperparameter Learning for Nonsmooth Regularized Imaging and ML Models.
Abstract: We study a bilevel optimization framework for hyperparameter learning in variational models, focusing on sparse regression and classification. Specifically, we use a weighted elastic-net regularizer, where feature-wise penalties are learned through a bilevel formulation. Our main contribution is a Forward–Backward (FB) reformulation of the nonsmooth lower-level problem that preserves its minimizers. This yields a bilevel objective composed with a locally Lipschitz solution map, enabling the use of generalized subdifferential calculus and efficient subgradient-based methods....
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