ABSTRACT. The COVID-19 pandemic has seen dramatic demand surges for hospital care that have placed a severe strain on health systems worldwide. As a result, policy makers are faced with the challenge of managing scarce hospital capacity so as to reduce the backlog of non-COVID patients whilst maintaining the ability to respond to any potential future increases in demand for COVID care. In this talk, we propose a nation-wide prioritization scheme that models each individual patient as a dynamic program whose states encode the patient's health and treatment condition, whose actions describe the available treatment options, whose transition probabilities characterize the stochastic evolution of the patient's health and whose rewards encode the contribution to the overall objectives of the health system. The individual patients' dynamic programs are coupled through constraints on the available resources, such as hospital beds, doctors and nurses. We show that near-optimal solutions to the emerging weakly coupled counting dynamic program can be found through a fluid approximation that gives rise to a linear program whose size grows gracefully in the problem dimensions. Our case study for the National Health Service in England shows how years of life can be gained and costs reduced by prioritizing specific disease types over COVID patients, such as injury & poisoning, diseases of the respiratory system, diseases of the circulatory system, diseases of the digestive system and cancer.

ABSTRACT. This talk will be devoted to a qualitative analysis of some aspects of the following question: consider a population that can access resources. What is the "best" way to spread these resources in the domain where the population lives? Of course, the word "best" is not univocal, and I will describe the features of two such optimisation problems: the first one is a spectral optimisation problem that is linked to the optimal survival ability of a population (which resources distribution yields the highest chance of survival for the population?), and the second one deals with the total population size (how can we get a maximal number of individuals by controlling the resources?). I will be giving an overview of the qualitative properties of these problems, with a strong emphasis on the most recent results related to the total population size.

This talk will be based on works carried out in collaboration with Grégoire Nadin, Yannick Privat and Domenec Ruiz-Balet.

ABSTRACT. New developments and environmental concerns change logistics practices, giving rise to new variants of the well known Vehicle Routing Problem (VRP). The classical VRP assumes a single period, a homogeneous fleet of vehicles, a single depot and a single trip per vehicle. Starting from some practical applications, we will present VRP variants obtained by relaxing some of these assumptions and discuss how to adapt the models and methods developed for VRP to these new variants.

ABSTRACT. Online feedback optimization refers to the design of feedback controllers that asymptotically steer a physical system to the solution of an optimization problem while respecting physical and operational constraints. For the considered optimization problem many parameters might be unknown, but one can rely on real-time measurements and the underlying physical system enforcing certain constraints. This problem setup is motivated by applications to electric power systems and has historic roots in communication networks and process control. In comparison to other optimization-based control strategies, transient optimality of trajectories is not the primary goal, and no predictive model, running costs or exogenous setpoints are required. Hence, one aims at controllers that require little model information, demand low computational cost, but that leverage real-time measurements. We design such controllers based on optimization algorithms that take the form of open and discontinuous dynamical systems. In this talk we discuss different algorithms such as projected gradient and saddle-point flows, their closed-loop stability when interconnected with physical systems, robustness properties, regularity conditions, and implementation aspects. Throughout the talk we demonstrate the potential of our methodology for real-time operation of power systems.

ABSTRACT. Non-orthogonal multiple access (NOMA) is a promising technology to increase the spectral efficiency and enable massive connectivity in future wireless networks. The principle of NOMA is to serve multiple users on the same frequency and time resource by superposing their signal in the power domain. One of the key challenges to achieve the full potential of NOMA is to solve the joint subcarrier and power allocation (JSPA) problem. To tackle this problem, we propose a generic optimization framework covering a large class of utility functions and practical constraints. In this framework, we divide the general JSPA problem into several sub-problems and develop algorithms taking advantage of each sub-problem’s specific properties. We also study their computational complexity and approximability. The generality and modularity of this framework allows to extend our algorithms to new constraints and scenarios.

ABSTRACT. Computing or approximating an optimal transport cost is rarely the sole goal when using OT in applications. In most cases the end goal relies instead on solving the OT problem and studying the differentiable properties of its solutions w.r.t. to arbitrary input variables. After a short introduction to optimal transport, I will present in this talk recent applications that highlight this necessity, as well as concrete algorithmic and programmatic solutions to handle such issues.

Relevant links: https://ott-jax.readthedocs.io/