AbstractWe study the function G(b) = inf{cx + dy ∣ Ax + By = b, x, y ⩾ 0 and x integer} under the assumptions that G(0) = 0 and A and B are matrices of rationals. G is defined for b ∈ Rm feasible, i.e., b for which the constraining conditions are consistent. We show that: 1.(1) There are constants C, D ⩾ 0 such that for any b, b' feasible and (x, y) with Ax + By = b; x,y⩾0 and x integer, there exist (x′, y′) with Ax′ + By′ = b′;x′,y′⩾0 and x′ integer, for which ∣(x, y) − (x′, y′)∣ ⩽ C∣b−b′∣ + D holds. In a pure integer program (i.e., for B empty) we can take D = 0.2.(2) G is piecewise polyhedral, with finitely many regions in any bounded set. In fact, we obtain a “normal form” for G which reveals the fact just cited as a consequence.3.(3) F...
We show that a 2-variable integer program, defined by m constraints involving coefficients with at m...
Generalized linear programming problems have been well solved by column generation and dual ascent p...
AbstractIt is shown how the dual of Fourier–Motzkin elimination can be applied to eliminating the co...
AbstractWe study the function G(b) = inf{cx + dy ∣ Ax + By = b, x, y ⩾ 0 and x integer} under the as...
AbstractRecent work has provided explicit formulas for the value function of a pure integer program,...
AbstractWe prove that the gap in optimal value, between a mixed-integer program in rationals and its...
AbstractIn an earlier report the concept of a mixed integer minimization model (MIMM) was defined an...
A mixed-integer program is an optimization problem where one is required to minimize a linear functi...
We introduce a general technique to create an extended formulation of a mixed-integer program. We ...
<p>Mixed-integer programming provides a natural framework for modeling optimization problems which r...
AbstractThis paper is a survey, with new results, of the algebraic approach to cutting-planes. The n...
This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces t...
This paper gives an introduction to a recently established link between the geometry of numbers and ...
AbstractIt is shown that every minimal valid inequality is generated by a subadditive function which...
This book is an elegant and rigorous presentation of integer programming, exposing the subject’s mat...
We show that a 2-variable integer program, defined by m constraints involving coefficients with at m...
Generalized linear programming problems have been well solved by column generation and dual ascent p...
AbstractIt is shown how the dual of Fourier–Motzkin elimination can be applied to eliminating the co...
AbstractWe study the function G(b) = inf{cx + dy ∣ Ax + By = b, x, y ⩾ 0 and x integer} under the as...
AbstractRecent work has provided explicit formulas for the value function of a pure integer program,...
AbstractWe prove that the gap in optimal value, between a mixed-integer program in rationals and its...
AbstractIn an earlier report the concept of a mixed integer minimization model (MIMM) was defined an...
A mixed-integer program is an optimization problem where one is required to minimize a linear functi...
We introduce a general technique to create an extended formulation of a mixed-integer program. We ...
<p>Mixed-integer programming provides a natural framework for modeling optimization problems which r...
AbstractThis paper is a survey, with new results, of the algebraic approach to cutting-planes. The n...
This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces t...
This paper gives an introduction to a recently established link between the geometry of numbers and ...
AbstractIt is shown that every minimal valid inequality is generated by a subadditive function which...
This book is an elegant and rigorous presentation of integer programming, exposing the subject’s mat...
We show that a 2-variable integer program, defined by m constraints involving coefficients with at m...
Generalized linear programming problems have been well solved by column generation and dual ascent p...
AbstractIt is shown how the dual of Fourier–Motzkin elimination can be applied to eliminating the co...