Compact vs. exponential-size LP relaxations

Compact vs. exponential-size LP relaxations

In this paper we introduce by means of examples a new technique for formulating compact (i.e. polynomial-size) LP relaxations in place of exponential-size models requiring separation algorithms. In the same vein as a celebrated theorem by Grotschel, Lovasz and Schrijver, we state the equivalence of compact separation and compact optimization. Among the examples used to illustrate our technique,...

Semidefinite Programming vs. LP Relaxations for Polynomial Programming

We consider the global minimization of a multivariate polynomial on a semi-algebraic set defined with polynomial inequalities. We then compare two hierarchies of relaxations, namely, LP relaxations based on products of the original constraints, in the spirit of the RLT procedure of Sherali and Adams (1990), and recent semidefinite programming (SDP) relaxations introduced by the author. The comp...

LP-relaxations for tree augmentation

In the Tree Augmentation problem the goal is to augment a tree T by a minimum size edge set F from a given edge set E such that T ∪ F is 2-edge-connected. The best approximation ratio known for the problem is 1.5. In the more general Weighted Tree Augmentation problem, F should be of minimum weight. Weighted Tree Augmentation admits several 2-approximation algorithms w.r.t. the standard cut-LP ...

LP relaxations and pruning for characteristic imsets

The geometric approach to learning a Bayesian network (BN) structure is based on the idea to represent every BN structure by a certain vector. Suitable such a zero-one vector representative is the characteristic imset, introduced in [20]. This concept allows one to re-formulate the task of finding the global maximum of a score over BN structures as an integer linear programming (ILP) problem. I...

Lecture 2: LP Relaxations, Randomized Rounding