A central result in the theory of integer optimization states that a system of linear diophantine equations Ax = b has no integral solution if and only if there exists a vector in the dual lattice, yT A integral such that yT b is fractional. We extend this result to systems that both have equations and inequalities {Ax = b, Cx ≤ d}. We show that a certificate of integral infeasibility is a line...

The proposed method for automatic knowledge extruction from large-scale data is bused on ideas of analysis of neighborhoods of ‘supporting” objects and construction of data covers by sets of hyperpurullelepipeds. A simple procedure to choose the supporting objects is applied. Knowledge extraction (logical regularities search) is bused on solution of special discrete linear optimization tusks as...

A linear program is typically specified by a matrix A together with two vectors b and c, where A is an n-by-d matrix, b is an n-vector and c is a d-vector. There are several canonical forms for defining a linear program using (A, b, c). One commonly used canonical form is: max cx s.t. Ax ≤ b and its dual min by s.t A y = c, y ≥ 0. In [Ren95b, Ren95a, Ren94], Renegar defined the condition number...

In this paper, we consider the multi-facility Weber location problem (MFWP) with uncertain location of demand points and transportation cost parameters. Equivalent formulations of its robust counterparts for both the Euclidean and block norms and interval and ellipsoidal uncertainty sets are given as conic linear optimization problems. 2014 Elsevier Inc. All rights reserved.

We give upper bounds on t-pebbling numbers of graphs of small diameter and investigate the relationships between these results and those relating to fractional pebbling. Furthermore, we present a connection between optimal pebbling and linear optimization and utilize this relationship in analyzing various graphs. We introduce the optimal fractional pebbling number of a graph and provide a combi...

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The theme of this paper is the application of linear analysis to simplify and extend convex analysis. The central problem treated is the standard convex program -minimize a convex function subject to inequality constraints on other convex functions. The present approach uses the support planes of the constraint region to transform the convex program into an equivalent linear program. Then the d...

A subdifferentiable global contact detection algorithm, the Supporting Separating Hyperplane (SSH) algorithm, based on the signed distance between supporting hyperplanes of two convex sets is developed. It is shown that for polyhedral sets, the SSH algorithm may be evaluated as a linear program, and that this linear program is always feasible and always subdifferentiable with respect to the con...