Gustavo Ponce

University of California Santa Barbara ,USA 

Aurea Martinez-Varela

Universidad de Vigo,Spain

Eduardo Casas 

Universidad de Cantabria-spain

 14:00h – 14:40h

Superlinear Convergence of a Semismooth Newton Method for some Optimization Problems with Applications to Control Theory

Let (X, S, μ) be a measure space with μ(X) < ∞. In this talk, we prove the superlinear convergence of a semismooth Newton method to solve the following abstract optimization problem:
(P)     min J(u) +k/2(//u//^2L2(X))
α≤u(x)≤β a.e.[μ]

,where κ > 0, −∞ ≤ α < β ≤ +∞, and J : Lp(X) → R is a function of

class C2 for some p ∈ [2, +∞). Many optimal control problems fall within this abstract formulation, such as distributed or boundary control problems and bilinear control problems associated with nonlinear elliptic or parabolic equations. We propose a superlinearly convergent semismooth Newton method to compute a local minimizer ̄u of (P) assuming that the no-gap second order sufficient optimality condition and the strict complementarity condition are fulfilled.

These assumptions are usually imposed to prove the superlinear or second order convergence of numerical algorithms for solving finite dimensional optimization problems. The translation of our algorithm to the case of optimal control problems governed by elliptic or parabolic semilinear equations is immediate.

Mejdi Azaiez

Bordeaux INP,France

14:50h – 15:30h

Least-Squares Pressure Recovery in Reduced Order Methods for Incompressible Flows

Victorita Dolean-Maini

Eindhoven University of Technology Department of Mathematics and Computer Science,Eindhoven, the Netherlands

14:00h – 14:40h

Fast Solution Methods for Wave Propagation Problems: From Classical Domain Decomposition Solvers to Learning

Wave propagation and scattering problems are of huge importance in many applications in science and engineering – e.g., in seismic and medical imaging and more generally in acoustics and electromagnetics. Large-scale simulations of those applications are one of the hard problems from a computational point of view since requires an interplay between the parsimonious but sufficiently accurate discretisation methods and more sophisticated solution methods. Our aim is to show on one side, how classical domain decomposition methods developed in the latest years coupled with carefully chosen discretisations can help in this endeavour. On the other side, we would like to propose some openings towards the very attractive package of approximation-solution-optimisation offered by the new methods in scientific machine learning.

Axel Osses

Departamento de Ingeniería Matemática, Center for Mathematical Modeling. Universidad de Chile, Chile.

14:50h – 15:30h

Direct and Inverse problems in heart muscle fibers identification

Gunther Uhlmann

Department of Mathematics, University of Washington, Seattle, WA, United States

14:00h – 14:40h

The Calderon Inverse Problem

Calderon’s inverse problem asks whether one can determine the
conductivity of a medium by making voltage and current measurements at
the boundary.  This question  arises in several areas of applications
including medical imaging and geophysics. I will report on some of the
progress that has been made on this problem since Calderon  proposed
it, including recent developments on similar problems for nonlinear
equations and nonlocal operators. We will also discuss several open problems.

François Delarue

Université Côte d’Azur, CNRS, Nice, France

14:50h – 15:30h

Selected Topics in Mean Field Control

Jone Apraiz

University of the Basque Country, Spain

14:00h – 14:40h

Observability and control of parabolic equations on networks

During the last decades, the use of networks has been very helpful and effective in the
study of pipes, neural systems, the flow of traffic on roads, the global economy or the
human circulatory systems.
In this talk I would like to show you a contribution to this area from the fields of control
theory and inverse problems. We will consider the propagation of diffusion on a network
with loops. Our objective is to control these networks by acting on the system that
models the process of the heat diffusion in them, both by open-loop and closed-loop
controls, extending in this way the results of [2] and [3] to networks with loops.
The observability of the entire network will be achieved under certain hypotheses about
the position of the observation domain. This will be done using a Carleman inequality.
Then, we will use that observability to prove the null controllability of the network and
to obtain the Lipschitz stability for an inverse problem consisting of retrieving a
stationary potential in the heat equation from measurements on the observation
domain.
This work has been done in collaboration with Jon Asier Bárcena-Petisco, from the
University of the Basque Country, and is based on the article [1].

References
[1] J. Apraiz and J. A. Bárcena-Petisco, Observability and control of parabolic equations
on networks with loops, Journal of Evolution Equations 23, 37, 2023,
https://doi.org/10.1007/s00028-023-00882-2 .
[2] J. A. Bárcena-Petisco, M. Cavalcante, G. M. Coclite, N. Nitti and E. Zuazua, Control of
hyperbolic and parabolic equations on networks and singular limits, hal-03233211
(2021).
[3] L. Ignat, A. F. Pazoto and L. Rosier, Inverse problem for the heat equation and the
Schrödinger equation on a tree, Inverse Prob. 28, 1, (2011), 015011.

Renato Iturriaga

CIMAT,Mexico

14:50h – 15:30h

Homographic minimal motions in the N body problem: Scattering and Instabilty