In this paper we consider an infinite relaxation of the mixed integer linear program with two integer variables, nonnegative continuous variables and two equality constraints, and we give a complete characterization of its facets. We also derive an analogous characterization of the facets of the underlying finite integer program.

Triplet-singlet spin relaxation in a vertical electrostatic quantum dot containing two interacting electrons is studied with a realistic model that includes the effects of finite thickness and screening. The spin relaxation mechanism is taken to be spin mixing via the part of the Dresselhaus Hamiltonian that is linear in the lateral momentum. The electron-electron interaction enhances relaxatio...

In this work, we present a Lagrangean relaxation of the hull-reformulation of discrete-continuous optimization problems formulated as linear generalized disjunctive programs (GDP). The proposed Lagrangean relaxation has three important properties. The first property is that it can be applied to any linear GDP. The second property is that the solution to its continuous relaxation always yields 0...

We present experimental results on the linear rheology of multiarm star/linear polymer mixtures, the latter having molecular weight much smaller than the star arm molecular weight. In such a case the linear chains act as ideal macromolecular solvents, which dilute entanglements of the arms. Using different star polymers we show that it is possible to account for this dilution and describe the l...

A disadvantage of the SDP (semidefinite programming) relaxation method for quadratic and/or combinatorial optimization problems lies in its expensive computational cost. This paper proposes a SOCP (second-order-cone programming) relaxation method, which strengthens the lift-and-project LP (linear programming) relaxation method by adding convex quadratic valid inequalities for the positive semid...

Deterministic annealing and relaxation labeling algorithms for classification and matching are presented and discussed. A new approach—self annealing—is introduced to bring deterministic annealing and relaxation labeling into accord. Self annealing results in an emergent linear schedule for winner-take-all and linear assignment problems. Self annihilation, a generalization of self annealing is ...

When variables of constraints of an 0−1 Integer Linear Program (ILP) is replaced by a weaker constraint such that each variable belongs to the interval [0, 1] (i.e. decimal) instead of fixed values {0, 1} (integers); then this relaxation generates a new Linear Programming problem. For example, the constraint xi ∈ {0, 1} becomes 0 ≤ xi ≤ 1. This relaxation technique is useful to convert an NP-ha...

Multigrid is widely used as an efficient solver for sparse linear systems arising from the discretization of elliptic boundary value problems. Linear relaxation methods like Gauss-Seidel and Red-Black Gauss-Seidel form the principal computational component of multigrid, and thus affect its efficiency. In the context of multigrid, these iterative solvers are executed for a small number of iterat...