On the Hardest Problem Formulations for the 0/1 Lasserre Hierarchy

Adam Kurpisz; Samuli Leppänen; Monaldo Mastrolilli

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arXiv · 1510.01891

On the Hardest Problem Formulations for the 0/1 Lasserre Hierarchy

Adam Kurpisz·Samuli Leppänen·Monaldo Mastrolilli

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Abstract

The Lasserre/Sum-of-Squares (SoS) hierarchy is a systematic procedure for constructing a sequence of increasingly tight semidefinite relaxations. It is known that the hierarchy converges to the 0/1 polytope in n levels and captures the convex relaxations used in the best available approximation algorithms for a wide variety of optimization problems. In this paper we characterize the set of 0/1 integer linear problems and unconstrained 0/1 polynomial optimization problems that can still have an integrality gap at level n-1. These problems are the hardest for the Lasserre hierarchy in this sense.

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Adam Kurpisz, Samuli Leppänen, Monaldo Mastrolilli. 2015-10-07. On the Hardest Problem Formulations for the 0/1 Lasserre Hierarchy. https://arxiv.org/abs/1510.01891

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