Hartvigsen, D. and E. Zemel, The complexity of lifted inequalities for the knapsack problem, Discrete Applied Mathematics 39 (1992) 11. 123. It is well known that one can obtain facets and valid inequalities for the knapsack polytope by lifting simple inequalities associated with minimal covers. We study the complexity of lifting. We show that recognizing integral lifted facets or valid inequal...

Günlük and Pochet [O. Günlük , Y. Pochet: Mixing mixed integer inequalities. Mathematical Programming 90(2001) 429-457] proposed a procedure to mix mixed integer rounding (MIR) inequalities. The mixed MIR inequalities define the convex hull of the mixing set {(y, . . . , y, v) ∈ Z × R+ : α1y + v ≥ βi, i = 1, . . . ,m} and can also be used to generate valid inequalities for general as well as se...

In this paper, we are concerned with random sampling of an n dimensional integral point on an (n−1) dimensional simplex according to a multivariate discrete distribution. We employ sampling via Markov chain and propose two “hit-and-run” chains, one is for approximate sampling and the other is for perfect sampling. We introduce an idea of alternating inequalities and show that a logarithmic sepa...

Let n k denote the number of times the kth largest distance occurs among a set S of n points. We show that if S is the set of vertices of a convex polygone in the euclidean plane, then n1+2n2~3n and n2<~n +n 1. Together with the well-known inequality n~<~n and the trivial inequalities n~>~O and n2>~O, all linear inequalities which are valid for n, n 1 and n2 are consequences of these. Similar r...

It is customary to formulate the inequalities of the "Verzerrungssatz" type for analytic functions w—f(z), schlicht in the unit circle, with reference to a specific normalization. The two normalizations mainly used are: (a) f(z) is finite in \z\ < 1 , /(O) = 0 , /'(O) = 1; (b) ƒ(z) has a pole at 2 = 0 with the residue 1. If we want to obtain inequalities which are independent of any particular ...

In this paper, we propose an inexact alternating direction method with square quadratic proximal  (SQP) regularization for  the structured variational inequalities. The predictor is obtained via solving SQP system  approximately  under significantly  relaxed accuracy criterion  and the new iterate is computed directly by an explicit formula derived from the original SQP method. Under appropriat...

Using formal logic, many iproblems from the general area of linear inequalities co~ be expressed in the elementary theory o f addition on the real numbers (EAR). We describe a method for eliminatit~ quantiflers in EAR which has been programmed arm demonstrate its usefulness in solving some problems related to linear programming. In the area o f mechanical mathematics this kind o f approach has ...

An algorithm for generating interpolants for formulas which are conjunctions of quadratic polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that quadratic polynomial inequalities can be linearized if they are concave. A generalization of Motzkin’s transposition theorem is proved, which is used to generate an interpolant between two mutu...

The fixed-charge transportation problem is an interesting problem in its own right. This paper further motivates its study by showing that it is both a special case and a strong relaxation of the big-bucket multi-item lot-sizing problem. We then provide a polyhedral analysis of the polynomially solvable special case in which the associated bipartite graph is a path. We give a O(n 3)-time optimi...