A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
Approximation of the Stability Number of a Graph via Copositive Programming
SIAM Journal on Optimization
An Explicit Equivalent Positive Semidefinite Program for Nonlinear 0-1 Programs
SIAM Journal on Optimization
Solving Standard Quadratic Optimization Problems via Linear, Semidefinite and Copositive Programming
Journal of Global Optimization
Semidefinite Programming vs. LP Relaxations for Polynomial Programming
Mathematics of Operations Research
Polynomial Programming: LP-Relaxations Also Converge
SIAM Journal on Optimization
LMI Approximations for Cones of Positive Semidefinite Forms
SIAM Journal on Optimization
Improved Bounds for the Crossing Numbers of Km,n and Kn
SIAM Journal on Discrete Mathematics
A PTAS for the minimization of polynomials of fixed degree over the simplex
Theoretical Computer Science - Approximation and online algorithms
Semidefinite representations for finite varieties
Mathematical Programming: Series A and B
On the computation of C* certificates
Journal of Global Optimization
A Variational Approach to Copositive Matrices
SIAM Review
Journal of Global Optimization
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The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO). It is NP-hard, and contains the maximum stable set problem in graphs as a special case. In this note, we show that the SQO problem may be reformulated as an (exponentially sized) linear program (LP). This reformulation also suggests a hierarchy of polynomial-time solvable LP's whose optimal values converge finitely to the optimal value of the SQO problem. The hierarchies of LP relaxations from the literature do not share this finite convergence property for SQO, and we review the relevant counterexamples.