Noticias en español
Optimal 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....
Read MoreA distributed proximal splitting method with linesearch for problems with locally Lipschitz gradients
Abstract: We consider finitely many agents over a connected network working cooperatively to solve a consensus optimization problem. Each agent owns a private convex cost function with a decomposable structure given by the sum of two terms, one smooth and one nonsmooth. In our distributed setting, no agent has direct access to the information of the overall network, but instead they can only communicate with their immediate neighbors. We propose a distributed primal-dual splitting method of proximal-gradient type that defines appropriate stepsizes by means of backtracking linesearch...
Read MoreRandomized block-coordinate descent beyond gradient global Lipschitz continuity
Abstract: Randomized block-coordinate algorithms are recognized to furnish efficient iterative schemes for addressing large-scale problems, especially when the computation of full derivatives entails substantial memory requirements and computational efforts. Classically, the convergence analysis of these methods relies on a standard assumption of global Lipschitz continuity of partial gradients of differentiable functions. This compromises its applicability to situations where gradient Lipschitz continuity is violated, for instance, in nonnegative matrix factorization or recovery of signals...
Read MoreNumerical solution of optimal control problems under uncertainty.
Abstract: The topic of this talk is a class of optimal control problems subject to uncertainty. We highlight some of the difficulties in the infinite-dimensional setting, which is of interest in physics- based models where a control belonging to a Banach space acts on a system described by a partial differential equation (PDE) with random inputs or parameters. We compare numerical approaches based on sample average approximation (SAA) and stochastic approximation (SA). The latter approach can be shown to perform competitively for applications in PDE-constrained optimization and numerical...
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