Related papers: On Computing the Copositive Minimum and its Repres…
We examine LDPC codes decoded using linear programming (LP). Four contributions to the LP framework are presented. First, a new method of tightening the LP relaxation, and thus improving the LP decoder, is proposed. Second, we present an…
A procedure and theoretical results are presented for the problem of determining a minimal robust positively invariant (RPI) set for a linear discrete-time system subject to unknown, bounded disturbances. The procedure computes, via the…
Given a parametric lattice with a basis given by polynomials in Z[t], we give an algorithm to construct an LLL-reduced basis whose elements are eventually quasi-polynomial in t: that is, they are given by formulas that are piecewise…
A new nonparametric estimator for Toeplitz covariance matrices is proposed. This estimator is based on a data transformation that translates the problem of Toeplitz covariance matrix estimation to the problem of mean estimation in an…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
The approximation of tensors is important for the efficient numerical treatment of high dimensional problems, but it remains an extremely challenging task. One of the most popular approach to tensor approximation is the alternating least…
In this paper, we establish the explicit lower bound estimates for the rank of universal quadratic forms in some certain families of real cubic fields under the condition of density one. The more general results that represent all multiples…
In this paper, we present an algorithm of simple exponential growth called COPOMATRIX for determining the copositivity of a real symmetric matrix. The core of this algorithm is a decomposition theorem, which is used to deal with simplicial…
Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…
The decomposition of tensors into simple rank-1 terms is key in a variety of applications in signal processing, data analysis and machine learning. While this canonical polyadic decomposition (CPD) is unique under mild conditions, including…
The main aim of this paper is to develop a new algorithm for computing nonnegative low rank tensor approximation for nonnegative tensors that arise in many multi-dimensional imaging applications. Nonnegativity is one of the important…
In these notes we discuss the procedure how to calculate nullvectors in general indecomposable representations which are encountered in logarithmic conformal field theories. In particular, we do not make use of any of the restrictions which…
We develop an algorithm that determines, for a given squarefree binary form $F$ with real coefficients, a smallest representative of its orbit under $\operatorname{SL}(2,\mathbb Z)$, either with respect to the Euclidean norm or with respect…
In order to generate prime implicants for a given cube (minterm), most of minimization methods increase the dimension of this cube by removing one literal from it at a time. But there are two problems of exponential complexity. One of them…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
A fast new algorithm is used compute the zeros of the quadratic character L-functions for all negative fundamental discriminants with absolute value 10^12<d<10^12+10^7. These are compared to the 1-level density, including various lower…
We consider a class of structured fractional minimization problems, in which the numerator part of the objective is the sum of a differentiable convex function and a convex non-smooth function, while the denominator part is a convex or…
Simple minimal but informationally complete positive operator-valued measures are constructed out of the expectation-value representation for qudits. Upon suitable modification, the procedure transforms any set of d^2 linearly independent…
By connecting the LU factorization and the Gram-Schmidt orthogonalization without any normalization, closed-forms for the coefficients of the ordinary least squares estimates are presented. Instead of using matrix inversion explicitly, each…
In order to formulate mathematical conjectures likely to be true, a number of base cases must be determined. However, many combinatorial problems are NP-hard and the computational complexity makes this research approach difficult using a…