Related papers: Reduction of Linear Programming to Linear Approxim…
This paper proposes a model, the linear model, for randomly generating logic programs with low density of rules and investigates statistical properties of such random logic programs. It is mathematically shown that the average number of…
We survey key techniques and results from approximation theory in the context of uniform approximations to real functions such as e^{-x}, 1/x, and x^k. We then present a selection of results demonstrating how such approximations can be used…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…
The rate vs. distance problem is a long-standing open problem in coding theory. Recent papers have suggested a new way to tackle this problem by appealing to a new hierarchy of linear programs. If one can find good dual solutions to these…
The linear programming method is applied to the space $\U_n(\C)$ of unitary matrices in order to obtain bounds for codes relative to the diversity sum and the diversity product. Theoretical and numerical results improving previously known…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We consider the problem of constructing an approximation of the Pareto curve associated with the multiobjective optimization problem $\min_{\mathbf{x} \in \mathbf{S}}\{ (f_1(\mathbf{x}), f_2(\mathbf{x})) \}$, where $f_1$ and $f_2$ are two…
This paper presents an algorithm to simulate Gaussian random vectors whose precision matrix can be expressed as a polynomial of a sparse matrix. This situation arises in particular when simulating Gaussian Markov random fields obtained by…
In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that…
Traditionally, there are several polynomial algorithms for linear programming including the ellipsoid method, the interior point method and other variants. Recently, Chubanov [Chubanov, 2015] proposed a projection and rescaling algorithm,…
We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job…
We present necessary and sufficient conditions for the termination of linear homogeneous programs. We also develop a complete method to check termination for this class of programs. Our complete characterization of termination for such…
We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…
We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed spaces. Based on such a representation, we study a fully piecewise linear vector…
This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results…
We obtain an analog of Shvedov theorem for convex multivariate approximation by algebras of continuous functions.
We propose a vector linear programming formulation for a non-stationary, finite-horizon Markov decision process with vector-valued rewards. Pareto efficient policies are shown to correspond to efficient solutions of the linear program, and…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…
The first aim of this paper is to show that any finite-dimensional reductive Lie algebra and its finite-dimensional completely reducible representation can be embedded into some PC Lie algebra. The second aim is to find the structure of a…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…