Related papers: NP-hardness of polytope M-matrix testing and relat…

Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…

In this paper, we prove the problem of stabbing a set of disjoint bends by a convex stabber to be NP-hard. We also consider the optimization version of the convex stabber problem and prove this problem to be APX-hard for sets of line…

We extend the concept of the m-weak group MP inverse of a square matrix to a rectangular matrix, called the W-weighted m-weak group MP inverse, which also unifies the W-weighted weak core inverse and W-weighted DMP inverse. Some properties,…

We investigate the symmetric inverse M-matrix problem from a geometric perspective. The central question in this geometric context is, which conditions on the k-dimensional facets of an n-simplex S guarantee that S has no obtuse dihedral…

Let a and x denote tuples of (jointly) freely noncommuting variables. A square matrix valued polynomial p in these variables is naturally evaluated at a tuple (A,X) of symmetric matrices with the result p(A,X) a square matrix. The…

This note presents a summary and review of various conditions and characterizations for matrix stability (in particular diagonal matrix stability) and matrix stabilizability.

We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are non-integrable. As a more sensitive integrability test, we propose the…

The matrix rank minimization problem has applications in many fields such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization…

We make an experimental comparison of methods for computing the numerical radius of an $n\times n$ complex matrix, based on two well-known characterizations, the first a nonconvex optimization problem in one real variable and the second a…

We consider discrete-time switching systems composed of a finite family of affine sub-dynamics. First, we recall existing results and present further analysis on the stability problem, the existence and characterization of compact…

The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…

The issues of robust stability for two types of uncertain fractional-order systems of order $\alpha \in (0,1)$ are dealt with in this paper. For the polytope-type uncertainty case, a less conservative sufficient condition of robust…

With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a…

We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…

We define dual-critical graphs as graphs having an acyclic orientation, where the indegrees are odd except for the unique source. We have very limited knowledge about the complexity of dual-criticality testing. By the definition the problem…

We present a new, scalable alternative to the structured singular value, which we call $\nu$, provide a convex upper bound, study their properties and compare them to $\ell_1$ robust control. The analysis relies on a novel result on the…

We are concerned with the tensor equation with an M-tensor or Z-tensor, which we call the M- tensor equation or Z-tensor equation respectively. We derive a necessary and sufficient condition for a Z (or M)-tensor equation to have…

This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for…

Recently, Hajirasouliha and Raphael (WABI 2014) proposed a model for deconvoluting mixed tumor samples measured from a collection of high-throughput sequencing reads. This is related to understanding tumor evolution and critical cancer…

Convex polyhedra are the basis for several abstractions used in static analysis and computer-aided verification of complex and sometimes mission critical systems. For such applications, the identification of an appropriate…