Some optimal inapproximability results
Journal of the ACM (JACM)
Global Optimization with Polynomials and the Problem of Moments
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
On the complexity of Schmüdgen's positivstellensatz
Journal of Complexity
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Minimizing Polynomials via Sum of Squares over the Gradient Ideal
Mathematical Programming: Series A and B
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 complexity of Putinar's Positivstellensatz
Journal of Complexity
Convexity in SemiAlgebraic Geometry and Polynomial Optimization
SIAM Journal on Optimization
Handelman rank of zero-diagonal quadratic programs over a hypercube and its applications
Journal of Global Optimization
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We consider the problem of minimizing a polynomial on the hypercube $[0,1]^n$ and derive new error bounds for the hierarchy of semidefinite programming approximations to this problem corresponding to the Positivstellensatz of Schmüdgen [Math. Ann., 289 (1991), pp. 203-206]. The main tool we employ is Bernstein approximations of polynomials, which also gives constructive proofs and degree bounds for positivity certificates on the hypercube.