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# A PTAS for the minimization of polynomials of fixed degree over the simplex

@article{Klerk2006APF, title={A PTAS for the minimization of polynomials of fixed degree over the simplex}, author={Etienne de Klerk and Monique Laurent and Pablo A. Parrilo}, journal={Theor. Comput. Sci.}, year={2006}, volume={361}, pages={210-225} }

- Published 2006 in Theor. Comput. Sci.
DOI:10.1016/j.tcs.2006.05.011

One may assume w.l.o.g. that p(x) is a homogeneous polynomial (form). Indeed, as observed in [2], if p(x) = ∑d l=0 pl(x), where pl(x) is homogeneous of degree l, then minimizing p(x) over ∆ is equivalent to minimizing the degree d form p(x) := ∑d l=0 pl(x)( ∑n i=1 xi) . Problem (1) is an NP-hard problem, already for forms of degree d = 2, as it contains the maximum stable set problem. Indeed, for a graph G with adjacency matrix A, the maximum size α(G) of a stable set in G can be expressed as 1… CONTINUE READING

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