Related papers: A note on approximating the nearest stable discret…
We propose a simple, scalable, and fast gradient descent algorithm to optimize a nonconvex objective for the rank minimization problem and a closely related family of semidefinite programs. With $O(r^3 \kappa^2 n \log n)$ random…
We introduce the notion of descriptor embedding for nonlinear systems and use it for the data-driven design of stabilizing controllers. Specifically, we provide sufficient data-dependent LMI conditions which, if feasible, return a…
A common data analysis task is the reduced-rank regression problem: $$\min_{\textrm{rank-}k \ X} \|AX-B\|,$$ where $A \in \mathbb{R}^{n \times c}$ and $B \in \mathbb{R}^{n \times d}$ are given large matrices and $\|\cdot\|$ is some norm.…
We investigate the complexity of solving stable or perturbation-resilient instances of $k$-Means and $k$-Median clustering in fixed dimension Euclidean metrics (more generally doubling metrics). The notion of stable (perturbation resilient)…
The paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In particular, in…
In this paper, we present the first general solution to the automatic reconfiguration problem of timed discrete-event systems. We extend the recursive forcible backtracking approach which had been already solved the automatic…
We introduce the notion of a stable instance for a discrete optimization problem, and argue that in many practical situations only sufficiently stable instances are of interest. The question then arises whether stable instances of NP--hard…
This paper addresses the classical problem of determining the set of possible states of a linear discrete-time system subject to bounded disturbances from measurements corrupted by bounded noise. These so-called uncertainty sets evolve with…
We first propose a decentralized proximal stochastic gradient tracking method (DProxSGT) for nonconvex stochastic composite problems, with data heterogeneously distributed on multiple workers in a decentralized connected network. To save…
This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…
Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…
In this paper, we propose a new approach to prove stability of non-linear discrete-time systems. After introducing the new concept of stability contractor, we show that the interval centred form plays a fundamental role in this context and…
Spectral clustering is a well-known technique which identifies $k$ clusters in an undirected graph with weight matrix $W\in\mathbb{R}^{n\times n}$ by exploiting its graph Laplacian $L(W)$, whose eigenvalues $0=\lambda_1\leq \lambda_2 \leq…
In this article we obtain an optimal best approximation type result for fully discrete approximations of the transient Stokes problem. For the time discretization we use the discontinuous Galerkin method and for the spatial discretization…
This paper discusses a general framework for designing robust state estimators for a class of discrete-time nonlinear systems. We consider systems that may be impacted by impulsive (sparse but otherwise arbitrary) measurement noise…
The work deals with two major topics concerning the numerical analysis of Runge-Kutta-like (RK-like) methods, namely their stability and order of convergence. RK-like methods differ from additive RK methods in that their coefficients are…
Decentralized optimization is a promising parallel computation paradigm for large-scale data analytics and machine learning problems defined over a network of nodes. This paper is concerned with decentralized non-convex composite problems…
This study introduces a novel estimation method for the entries and structure of a matrix $A$ in the linear factor model $\mathbf{X} = A\textbf{Z} + \textbf{E}$. This is applied to an observable vector $\mathbf{X} \in \mathbb{R}^d$ with…
The main objective of the present paper is to construct a new class of space-time discretizations for the stochastic $p$-Stokes system and analyze its stability and convergence properties. We derive regularity results for the approximation…