Related papers: The convergence problem for dissipative autonomous…
We are interested in optimally driving a dynamical system that can be influenced by exogenous noises. This is generally called a Stochastic Optimal Control (SOC) problem and the Dynamic Programming (DP) principle is the natural way of…
We develop a necessary stochastic maximum principle for a finite-dimensional stochastic control problem in infinite horizon under a polynomial growth and joint monotonicity assumption on the coefficients. The second assumption generalizes…
Most of the models leading to a current state of cosmic accelerated expansion fail to address the coincidence problem, i.e., that the dark energy density and the energy density of the matter fluid are of the same order precisely today. We…
Optimization tasks are crucial in statistical machine learning. Recently, there has been great interest in leveraging tools from dynamical systems to derive accelerated and robust optimization methods via suitable discretizations of…
In this contribution, we present a full overview of the continuous stochastic gradient (CSG) method, including convergence results, step size rules and algorithmic insights. We consider optimization problems in which the objective function…
This Ph.D. thesis is divided in two parts. The first one concerns the equilibrium properties of glassy systems. Some aspects of the phenomenology of glasses and of theories attempting to describe them are reviewed in chapter 1. A study of…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
This work is concerned with ($N$-component) hyperbolic system of balance laws in arbitrary space dimensions. Under entropy dissipative assumption and the Shizuta-Kawashima algebraic condition, a general theory on the well-posedness of…
This paper deals with the approximation of the spectrum of linear and nonautonomous delay differential equations through the reduction of the relevant evolution semigroup from infinite to finite dimension. The focus is placed on classic…
The aim of this paper is to share with the mathematical community a list of 33 problems that I have found along the years during my research. I believe that it is worth to think about them and, hopefully, it will be possible either to solve…
Functions that are not differentiable in the classical sense have become a central tool in modern mathematical models for imaging, inverse problems, machine learning, and optimal control of differential equations. These models are…
Many fields of science and engineering require finding eigenvalues and eigenvectors of large matrices. The solutions can represent oscillatory modes of a bridge, a violin, the disposition of electrons around an atom or molecule, the…
The recently proposed definition of complexity for static and spherically symmetric self--gravitating systems [1], is extended to the fully dynamic situation. In this latter case we have to consider not only the complexity factor of the…
In this paper we prove convergence results for homogenization problem for solutions of partial differential system with rapidly oscillating Dirichlet data. Our method is based on analysis of oscillatory integrals. In the uniformly convex…
We study the characterization of several distance problems for linear differential-algebraic systems with dissipative Hamiltonian structure. Since all models are only approximations of reality and data are always inaccurate, it is an…
The aim of this paper is to study the finite-dimensional approximations of the nonautonomous lattice dynamical systems of the form $u_{i}'=\nu (u_{i-1}-2u_i+u_{i+1})-\lambda u_{i}+F(u_i)+f_{i}(t)\ (i\in \mathbb Z)\ (*)$. We show that the…
We analyze the complexity of biased stochastic gradient methods (SGD), where individual updates are corrupted by deterministic, i.e. biased error terms. We derive convergence results for smooth (non-convex) functions and give improved rates…
This paper focuses on applying entropic mirror descent to solve linear systems, where the main challenge for the convergence analysis stems from the unboundedness of the domain. To overcome this without imposing restrictive assumptions, we…
In the first part of the paper we consider accelerated first order optimization method for convex functions with $L$-Lipschitz-continuous gradient, that is able to automatically adapts to problems which satisfies Polyak-{\L}ojasiewicz…
In this paper an approach is proposed to represent a class of dissipative mechanical systems by corresponding infinite-dimensional Hamiltonian systems. This approach is based upon the following structure: for any non-conservative classical…