We study the lift-and-project rank of the stable set polytope of graphs with respect to the Lovász–Schrijver SDP operator \( \text{LS}_+ \) applied to the fractional stable set polytope. In particular, we show that for every positive integer \( \ell \), the smallest possible graph with \( \text{LS}_+ \)-rank \( \ell \) contains \( 3\ell … Read more
This paper introduces HALLaR, a new first-order method for solving large-scale semidefinite programs (SDPs) with bounded domain. HALLaR is an inexact augmented Lagrangian (AL) method where the AL subproblems are solved by a novel hybrid low-rank (HLR) method. The recipe behind HLR is based on two key ingredients: 1) an adaptive inexact proximal point method … Read more
We describe a conic interior point decomposition approach for solving a large scale semidefinite programs (SDP) whose primal feasible set is bounded. The idea is to solve such an SDP using existing primal-dual interior point methods, in an iterative fashion between a {\em master problem} and a {\em subproblem}. In our case, the master problem … Read more