A note on the Lovasz-Schrijver Semidefinite Programming Relaxation for Binary Integer Programs

TL;DR

This paper explicitly formulates the Lovasz-Schrijver SDP relaxation for binary integer programs, providing a tighter upper-bound than linear programming relaxations, with implications for combinatorial and network optimization.

Contribution

It presents an explicit primal-standard form of the Lovasz-Schrijver SDP relaxation for BIP problems, enhancing the theoretical understanding and potential solution quality.

Findings

Provides a tighter upper-bound than LP relaxation

Explicit formulation of the Lovasz-Schrijver SDP relaxation

Implications for graph and network optimization

Abstract

Binary Integer Programming (BIP) problems are of interest due in part to the difficulty they pose and because of their various applications, including those in graph theory, combinatorial optimization and network optimization. In this note, we explicitly state the Lovasz-Schrijver Semidefinite Programming (SDP) relaxation (in primal-standard form) for a BIP problem, a relaxation that yields a tighter upper-bound than the canonical Linear Programming relaxation.