Related papers: Approximating the Real Structured Stability Radius…

This paper concerns the problem of matrix completion, which is to estimate a matrix from observations in a small subset of indices. We propose a calibrated spectrum elastic net method with a sum of the nuclear and Frobenius penalties and…

The low-rank matrix approximation problem is ubiquitous in computational mathematics. Traditionally, this problem is solved in spectral or Frobenius norms, where the accuracy of the approximation is related to the rate of decrease of the…

The convolutional sparse model has recently gained increasing attention in the signal and image processing communities, and several methods have been proposed for solving the pursuit problem emerging from it -- in particular its convex…

Implicit inverse problems, in which noisy observations of a physical quantity are used to infer a nonlinear functional applied to an associated function, are inherently ill posed and often exhibit non uniqueness of solutions. Such problems…

We consider in this paper the problem of noisy 1-bit matrix completion under a general non-uniform sampling distribution using the max-norm as a convex relaxation for the rank. A max-norm constrained maximum likelihood estimate is…

Pseudospectral analysis is fundamental for quantifying the sensitivity and transient behavior of nonnormal matrices, yet its computational cost scales cubically with dimension, rendering it prohibitive for large-scale systems. While…

The ability to resolve detail in the object that is being imaged, named by resolution, is the core parameter of an imaging system. Super-resolution is a class of techniques that can enhance the resolution of an imaging system and even…

Graph matching, typically formulated as a Quadratic Assignment Problem (QAP), seeks to establish node correspondences between two graphs. To address the NP-hardness of QAP, some existing methods adopt projection-based relaxations that embed…

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…

This paper addresses the problem of finding the closest generalized essential matrix from a given $6\times 6$ matrix, with respect to the Frobenius norm. To the best of our knowledge, this nonlinear constrained optimization problem has not…

Meaningful comparison between sets of observations often necessitates alignment or registration between them, and the resulting optimization problems range in complexity from those admitting simple closed-form solutions to those requiring…

A new measure to characterize stability of complex dynamical systems against large perturbation is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable to disrupt the system and switch it…

This paper studies the Lagrange stabilization of a class of nonlinear systems whose linear part has a singular system matrix and which have multiple periodic (in state) nonlinearities. Both state and output feedback Lagrange stabilization…

We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…

Sparsity-based methods are widely used in machine learning, statistics, and signal processing. There is now a rich class of structured sparsity approaches that expand the modeling power of the sparsity paradigm and incorporate constraints…

A method is presented for tracing the locus of a specific peak in the frequency response under variation of a parameter. It is applicable to periodic, steady-state vibrations of harmonically forced nonlinear mechanical systems. It operates…

This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…

This paper is devoted to the development of adaptive control schemes for uncertain discrete-time systems, which guarantee robust, global, exponential convergence to the desired equilibrium point of the system. The proposed control scheme…

Opacity is a notion that describes an eavesdropper's inability to estimate a system's 'secret' states by observing the system's outputs. In this paper, we propose algorithms to compute the minimum sparse perturbation to be added to a system…

We consider the design of fast and reliable neural network (NN)-based approximations of traditional stabilizing controllers for linear systems with polytopic uncertainty, including control laws with variable structure and those based on a…