Related papers: Data-driven optimal approximation on Hardy spaces …
Numerically computing global policies to optimal control problems for complex dynamical systems is mostly intractable. In consequence, a number of approximation methods have been developed. However, none of the current methods can quantify…
In a Hilbert setting, we introduce a new dynamical system and associated algorithms for solving monotone inclusions by rapid methods. Given a maximal monotone operator $A$, the evolution is governed by the time dependent operator $I -(I +…
The need for multimodal data integration arises naturally when multiple complementary sets of features are measured on the same sample. Under a dependent multifactor model, we develop a fully data-driven orchestrated approximate message…
In this paper, we consider a network of agents that jointly aim to minimise the sum of local functions subject to coupling constraints involving all local variables. To solve this problem, we propose a novel solution based on a primal-dual…
Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit…
We develop a principled approach to obtain exact computer-aided worst-case guarantees on the performance of second-order optimization methods on classes of univariate functions. We first present a generic technique to derive interpolation…
In Part I, a novel Galerkin-type method for finite dimensional approximations of transfer functions in Hardy space was developed based on approximation by simple poles. In Part II, this approximation is applied to system level synthesis, a…
We consider the problem of optimal recovery of an element $u$ of a Hilbert space $\mathcal{H}$ from $m$ measurements obtained through known linear functionals on $\mathcal{H}$. Problems of this type are well studied \cite{MRW} under an…
Multi-objective optimization problems are ubiquitous in real-world science, engineering and design optimization problems. It is not uncommon that the objective functions are as a black box, the evaluation of which usually involve…
In this paper, further extensions of the result of the paper "A successive approximation method in functional spaces for hierarchical optimal control problems and its application to learning, arXiv:2410.20617 [math.OC], 2024" concerning a…
Variational data assimilation technique applied to identification of optimal approximations of derivatives near boundary is discussed in frames of one-dimensional wave equation. Simplicity of the equation and of its numerical scheme allows…
This paper studies an optimal control problem for continuous-time stochastic systems subject to reachability objectives specified in a subclass of metric interval temporal logic specifications, a temporal logic with real-time constraints.…
We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented,…
The rapid advancements in high-dimensional statistics and machine learning have increased the use of first-order methods. Many of these methods can be regarded as instances of the proximal point algorithm. Given the importance of the…
We aim to create the highest possible quality of treatment-control matches for categorical data in the potential outcomes framework. Matching methods are heavily used in the social sciences due to their interpretability, but most matching…
An important mathematical tool in the analysis of dynamical systems is the approximation of the reach set, i.e., the set of states reachable after a given time from a given initial state. This set is difficult to compute for complex systems…
Data-sensitive metrics adapt distances locally based the density of data points with the goal of aligning distances and some notion of similarity. In this paper, we give the first exact algorithm for computing a data-sensitive metric called…
We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit…
We consider a wide class of semi linear Hamiltonian partial differential equa- tions and their approximation by time splitting methods. We assume that the nonlinearity is polynomial, and that the numerical tra jectory remains at least uni-…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…