A Lagrange decomposition based Branch and Bound algorithm for the Optimal Mapping of Cloud Virtual Machines

One of the challenges of cloud computing is to optimally and efficiently assign virtual machines to physical machines. The aim of telecommunication operators is to mini- mize the mapping cost while respecting constraints regarding location, assignment and capacity. In this paper we first propose an exact formulation leading to a 0-1 bilinear constrained problem. Then … Read more

A Note on Linear On/Off Constraints

This note studies compact representations of linear on/off constraints in mixed-integer linear optimization. A characterization of the convex hull of linear disjunctions is given in the space of original variables. This result can improve formulations of mixed-integer linear programs featuring on/off constraints by reducing the integrality gap in a Branch and Bound approach. Citation @article{, … Read more

An Outer-Inner Approximation for separable MINLPs

A common structure in convex mixed-integer nonlinear programs is separable nonlinear functions. In the presence of such structures, we propose three improvements to the outer approximation algorithms. The first improvement is a simple extended formulation, the second is a refined outer approximation, and the third is a heuristic inner approximation of the feasible region. These … Read more

An Outer-Inner Approximation for separable MINLPs

A common structure in convex mixed-integer nonlinear programs is additively separable nonlinear functions consisting of a sum of univariate functions. In the presence of such structures, we propose three improvements to the classical Outer Approximation algorithms that exploit separability. The first improvement is a simple extended formulation. The second a refined outer approximation. Finally, the … Read more

Robust capacity expansion solutions for telecommunication networks with uncertain demands

We consider the capacity planning of telecommunication networks with linear investment costs and uncertain future traffic demands. Transmission capacities must be large enough to meet, with a high quality of service, the range of possible demands, after adequate routings of messages on the created network. We use the robust optimization methodology to balance the need … Read more

Mixed Integer NonLinear Programs featuring “On/Off ” constraints: convex analysis and applications

We call ”on/off” constraint an algebraic constraint that is activated if and only if a corresponding boolean variable is turned ”on” or equal to 1. Our main subject of interest is to derive tight convex formulations of Mixed Integer NonLinear Programs (MINLPs) featuring ”on/off” constraints. We study the simple set defined by one ”on/off” constraint … Read more

A Proximal Cutting Plane Method Using Chebychev Center for Nonsmooth Convex Optimization

An algorithm is developed for minimizing nonsmooth convex functions. This algorithm extends Elzinga-Moore cutting plane algorithm by enforcing the search of the next test point not too far from the previous ones, thus removing compactness assumption. Our method is to Elzinga-Moore’s algorithm what a proximal bundle method is to Kelley’s algorithm. Instead of lower approximations … Read more