Grothendieck inequalities for semidefinite programs with rank constraint
Optimization and Control
2014-06-03 v2 Data Structures and Algorithms
Combinatorics
Functional Analysis
Abstract
Grothendieck inequalities are fundamental inequalities which are frequently used in many areas of mathematics and computer science. They can be interpreted as upper bounds for the integrality gap between two optimization problems: a difficult semidefinite program with rank-1 constraint and its easy semidefinite relaxation where the rank constrained is dropped. For instance, the integrality gap of the Goemans-Williamson approximation algorithm for MAX CUT can be seen as a Grothendieck inequality. In this paper we consider Grothendieck inequalities for ranks greater than 1 and we give two applications: approximating ground states in the n-vector model in statistical mechanics and XOR games in quantum information theory.
Cite
@article{arxiv.1011.1754,
title = {Grothendieck inequalities for semidefinite programs with rank constraint},
author = {Jop Briet and Fernando Mario de Oliveira Filho and Frank Vallentin},
journal= {arXiv preprint arXiv:1011.1754},
year = {2014}
}
Comments
22 pages