Approximation of the Stability Number of a Graph via Copositive Programming
SIAM Journal on Optimization
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Solving Standard Quadratic Optimization Problems via Linear, Semidefinite and Copositive Programming
Journal of Global Optimization
An Explicit Exact SDP Relaxation for Nonlinear 0-1 Programs
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0--1 Programming
Mathematics of Operations Research
Optimization of Polynomials on Compact Semialgebraic Sets
SIAM Journal on Optimization
Strengthened semidefinite programming bounds for codes
Mathematical Programming: Series A and B
New code upper bounds from the Terwilliger algebra and semidefinite programming
IEEE Transactions on Information Theory
Simple ingredients leading to very efficient heuristics for the maximum clique problem
Journal of Heuristics
Exploiting equalities in polynomial programming
Operations Research Letters
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Lovász and Schrijver [9] have constructed semidefinite relaxations for the stable set polytope of a graph G = (V,E) by a sequence of lift-and-project operations; their procedure finds the stable set polytope in at most α(G) steps, where α(G) is the stability number of G. Two other hierarchies of semidefinite bounds for the stability number have been proposed by Lasserre [4],[5] and by de Klerk and Pasechnik [3], which are based on relaxing nonnegativity of a polynomial by requiring the existence of a sum of squares decomposition. The hierarchy of Lasserre is known to converge in α(G) steps as it refines the hierarchy of Lovász and Schrijver, and de Klerk and Pasechnik conjecture that their hierarchy also finds the stability number after α(G) steps. We prove this conjecture for graphs with stability number at most 8 and we show that the hierarchy of Lasserre refines the hierarchy of de Klerk and Pasechnik.