## New Convex Relaxations for the Maximum Cut . . . (2001)

### BibTeX

@MISC{Anjos01newconvex,

author = {Miguel Nuno Ferreira Fialho dos Anjos},

title = {New Convex Relaxations for the Maximum Cut . . . },

year = {2001}

}

### OpenURL

### Abstract

It is well known that many of the optimization problems which arise in applica-tions are “hard”, which usually means that they are NP-hard. Hence much research has been devoted to finding “good” relaxations for these hard problems. Usually a “good” relaxation is one which can be solved (either exactly or within a prescribed numerical tolerance) in polynomial-time. Nesterov and Nemirovskii showed that by this criterion, many convex optimization problems are good relaxations. This thesis presents new convex relaxations for two such hard problems, namely the Maximum-Cut (Max-Cut) problem and the VLSI (Very Large Scale Integration of electronic circuits) layout problem. We derive and study the properties of two new strengthened semidefinite pro-