Why is maximum clique often easy in practice?

JL Walteros, A Buchanan - Operations Research, 2020 - pubsonline.informs.org
To this day, the maximum clique problem remains a computationally challenging problem.
Indeed, despite researchers' best efforts, there exist unsolved benchmark instances with …

On integrality in semidefinite programming for discrete optimization

F De Meijer, R Sotirov - SIAM Journal on Optimization, 2024 - SIAM
It is well known that by adding integrality constraints to the semidefinite programming (SDP)
relaxation of the max-cut problem, the resulting integer semidefinite program is an exact …

[HTML][HTML] On the Lovász theta function and some variants

L Galli, AN Letchford - Discrete Optimization, 2017 - Elsevier
The Lovász theta function of a graph is a well-known upper bound on the stability number. It
can be computed efficiently by solving a semidefinite program (SDP). Actually, one can …

Set-completely-positive representations and cuts for the max-cut polytope and the unit modulus lifting

F Jarre, F Lieder, YF Liu, C Lu - Journal of Global Optimization, 2020 - Springer
This paper considers a generalization of the “max-cut-polytope” conv {\xx^ T ∣ x ∈ R^ n,\|
x_k|= 1\hbox for\1 ≤ k ≤ n\} conv xx T∣ x∈ R n,| xk|= 1 for 1≤ k≤ n in the space of real …

Simplified semidefinite and completely positive relaxations

F Lieder - Operations Research Letters, 2015 - Elsevier
This paper is concerned with completely positive and semidefinite relaxations of quadratic
programs with linear constraints and binary variables as presented by Burer. It observes that …

[引用][C] Set-Completely-Positive Representations and Cuts for the Max-Cut Polytope and the Unit Modulus Lifting