A parametric integer programming algorithm for bilevel mixed integer programs

We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and mixed integer bilevel problems. For the mixed integer case where the leader's variables are continuous, our algorithm also detects whether the infimum cost fails to be attained, a difficulty that has been identified but not directly addressed in the literature. In this case it yields a ``better than fully polynomial time'' approximation scheme with running time polynomial in the logarithm of the relative precision. For the pure integer case where the leader's variables are integer, and hence optimal solutions are guaranteed to exist, we present two algorithms which run in polynomial time when the total number of variables is fixed.Comment: 11 page

On computational search for optimistic solutions in bilevel problems

Bilevel programming, Optimistic solution, Nonconvex optimization problems, Local search, Global search, Computational simulation,

CMS physics technical design report: Addendum on high density QCD with heavy ions

This report presents the capabilities of the CMS experiment to explore the rich heavy-ion physics programme offered by the CERN Large Hadron Collider (LHC). The collisions of lead nuclei at energies ,will probe quark and gluon matter at unprecedented values of energy density. The prime goal of this research is to study the fundamental theory of the strong interaction - Quantum Chromodynamics (QCD) - in extreme conditions of temperature, density and parton momentum fraction (low-x). This report covers in detail the potential of CMS to carry out a series of representative Pb-Pb measurements. These include "bulk" observables, (charged hadron multiplicity, low pT inclusive hadron identified spectra and elliptic flow) which provide information on the collective properties of the system, as well as perturbative probes such as quarkonia, heavy-quarks, jets and high pT hadrons which yield "tomographic" information of the hottest and densest phases of the reaction.0info:eu-repo/semantics/publishe