Related papers: Computing the Pseudospectral Abscissa of Time-Dela…
We propose an SDP-based framework to address the stabilization of input delay systems while taking into account dissipative constraints. A key to our approach is the introduction of the concept of parameterized linear dynamical state…
Delayed target response in synthetic aperture radar (SAR) imaging can be obscured by the range-delay ambiguity and speckle. To analyze the range-delay ambiguity, one extends the standard SAR formulation and allows both the target…
Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
In this paper, we investigate a general class of stochastic gradient descent (SGD) algorithms, called Conditioned SGD, based on a preconditioning of the gradient direction. Using a discrete-time approach with martingale tools, we establish…
We introduce new variants of classical regression-based algorithms for optimal stopping problems based on computation of regression coefficients by Monte Carlo approximation of the corresponding $L^2$ inner products instead of the…
In scalable machine learning systems, model training is often parallelized over multiple nodes that run without tight synchronization. Most analysis results for the related asynchronous algorithms use an upper bound on the information…
In this article, we introduce a general theoretical framework to analyze non-consistent approximations of the discrete eigenmodes of a self-adjoint operator. We focus in particular on the discrete eigenvalues laying in spectral gaps. We…
We consider the problem of asynchronous stochastic optimization, where an optimization algorithm makes updates based on stale stochastic gradients of the objective that are subject to an arbitrary (possibly adversarial) sequence of delays.…
In this paper, we consider the nonsmooth convex optimization problems over the fixed point constraint sets of firmly nonexpansive operators. To find an optimal solution of the problem, we present an iterative method based on the hybrid…
Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…
Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…
In this paper, stability analysis of time delay systems is considered based on decomposition of the systems to subsystems. The decomposition process needs matrices of these systems to be simultaneously block triangularize. We show that a…
This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction…
In this paper, we study the stochastic optimal control problem for control system with time-varying delay. The corresponding stochastic differential equation is a kind of stochastic differential delay equation. We prove the existence and…
This paper presents a first-order distributed algorithm for solving a convex semi-infinite program (SIP) over a time-varying network. In this setting, the objective function associated with the optimization problem is a summation of a set…
Spectral embedding based on the Singular Value Decomposition (SVD) is a widely used "preprocessing" step in many learning tasks, typically leading to dimensionality reduction by projecting onto a number of dominant singular vectors and…
We consider the problem of estimating the discrete clustering structures under the Sub-Gaussian Mixture Model. Our main results establish a hidden integrality property of a semidefinite programming (SDP) relaxation for this problem: while…
Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…
This chapter presents a dynamical systems point of view of the study of systems with delays. The focus is on how advanced tools from bifurcation theory, as implemented for example in the package DDE-BIFTOOL, can be applied to the study of…