Abstract
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.
| Original language | English |
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| Pages (from-to) | 3104-3120 |
| Journal | SIAM Journal on Optimization |
| Volume | 20 |
| Issue number | 6 |
| Publication status | Published - 2010 |