Related papers: Error Bound for the Linear Complementarity Problem…
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear…
In this paper, to the best of our knowledge, we make the first attempt at studying the parametric semilinear elliptic eigenvalue problems with the parametric coefficient and some power-type nonlinearities. The parametric coefficient is…
In many problems, the inputs arrive over time, and must be dealt with irrevocably when they arrive. Such problems are online problems. A common method of solving online problems is to first solve the corresponding linear program, and then…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
This paper is concerned with the two--phase obstacle problem, a type of a variational free boundary problem. We recall the basic estimates of Repin and Valdman (2015) and verify them numerically on two examples in two space dimensions. A…
In the first part of this study, a convex-constrained penalized formulation was studied for a class of constant modulus (CM) problems. In particular, the error bound techniques were shown to play a vital role in providing exact penalization…
This paper is concerned with the derivation of conforming and non-conforming functional a posteriori error estimates for elliptic boundary value problems in exterior domains. These estimates provide computable and guaranteed upper and lower…
Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of…
The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…
We study the behavior of simple principal pivoting methods for the P-matrix linear complementarity problem (P-LCP). We solve an open problem of Morris by showing that Murty's least-index pivot rule (under any fixed index order) leads to a…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
We consider the low rank matrix completion problem over finite fields. This problem has been extensively studied in the domain of real/complex numbers, however, to the best of authors' knowledge, there exists merely one efficient algorithm…
The following problem is considered: given a joint distribution $P_{XY}$ and an event $E$, bound $P_{XY}(E)$ in terms of $P_XP_Y(E)$ (where $P_XP_Y$ is the product of the marginals of $P_{XY}$) and a measure of dependence of $X$ and $Y$.…
An uniform LP duality is an useful property of conic matrix systems. A consistent linear conic optimization problem yields uniform LP duality if for any linear cost function, for which the primal problem has finite optimal value, the…
We investigate the relation between the girth and the guaranteed error correction capability of $\gamma$-left regular LDPC codes when decoded using the bit flipping (serial and parallel) algorithms. A lower bound on the number of variable…
The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…
In this paper, a general algorithm is proposed for rate analysis and code design of linear index coding problems. Specifically a solution for minimum rank matrix completion problem over finite fields representing the linear index coding…
In this paper, we study the linear complementarity problems on the monotone extended second order cones. We demonstrate that the linear complementarity problem on the monotone extended second order cone can be converted into a mixed…
In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial…