Mazanti, Guilherme Boussaada, Islam Niculescu, Silviu-Iulian Chitour, Yacine

It has been observed in several recent works that, for some classes of linear time-delay systems, spectral values of maximal multiplicity are dominant, a property known as multiplicity-induced-dominancy (MID). This paper starts the investigation of whether MID holds for delay differential-algebraic systems by considering a single-delay system compo...

Swikir, Abdalla Girard, Antoine Zamani, Majid

Symbolic models have been used as the basis of a systematic framework to address control design of several classes of hybrid systems with sophisticated control objectives. However, results available in the literature are not concerned with impulsive systems which are an important modeling framework of many applications. In this paper, we provide an...

Bonnet, Benoît Frankowska, Hélène

In this article, we propose a general framework for the study of differential inclusions in the Wasserstein space of probability measures. Based on earlier geometric insights on the structure of continuity equations, we define solutions of differential inclusions as absolutely continuous curves whose driving velocity fields are measurable selection...

Le Thi, Hoai An Le, Hoai Minh Pham Dinh, Tao Nguyen, Ngoc Thanh Quynh, Tran Duc Le, Luong Vuong Nguyen, Quang Thuan Tran, Duc Quynh Thuan, Nguyen Quang Anh, Nguyen Duc
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Kiedanski, Diego Bušić, Ana Kofman, Daniel ORDA, Ariel

Local energy generation as well as local energy storage represent key opportunities for energy transition. Nevertheless , their massive deployment is being delayed mainly due to cost reasons. Sharing resources at the local level enables not only reducing these costs significantly, but also to further optimize the cost of the energy exchanged with p...

Cherkaoui, Hamza Sulam, Jeremias Moreau, Thomas

Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the 1-norm of the first order derivative of the estimated signal. The resulting optimization problem is usually solved using iterative algorithms such as proximal gradient descent or primal-dual algorithms such as augmented Lagrangian...

Aubin-Frankowski, Pierre-Cyril Szabó, Zoltán

Shape constraints (such as non-negativity, monotonicity, convexity) play a central role in a large number of applications, as they usually improve performance for small sample size and help interpretability. However enforcing these shape requirements in a hard fashion is an extremely challenging problem. Classically, this task is tackled (i) in a s...

Bolte, Jerome Pauwels, Edouard

Automatic differentiation, as implemented today, does not have a simple mathematical model adapted to the needs of modern machine learning. In this work we articulate the relationships between differentiation of programs as implemented in practice and differentiation of nonsmooth functions. To this end we provide a simple class of functions, a nons...

Marushkevych, Dmytro Popier, Alexandre
Published in
Probability, Uncertainty and Quantitative Risk

We use the functional Itô calculus to prove that the solution of a BSDE with singular terminal condition verifies at the terminal time: liminft→TY(t)=ξ=Y(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\odds...

Ghattassi, Mohamed Laleg, Taous-Meriem Vivalda, Jean-Claude

This paper discusses the mathematical properties of a recently developed mathematical model of a direct contact membrane distillation system. The model consists of two-dimensional advection diffusion system coupled at the boundary. A semi-group framework is used to analyze the model. First, the infinitesimal generator operator and its properties ar...