## A Complete Characterization of the Gap between Convexity and SOS-Convexity

- Amir Ali Ahmadi, Pablo A. Parrilo
- SIAM Journal on Optimization
- 2013

@article{Lasserre2010CertificatesOC, title={Certificates of convexity for basic semi-algebraic sets}, author={Jean B. Lasserre}, journal={Appl. Math. Lett.}, year={2010}, volume={23}, pages={912-916} }

- Published 2010 in Appl. Math. Lett.
DOI:10.1016/j.aml.2010.04.009

We provide two certificates of convexity for arbitrary basic closed semi-algebraic sets of R. The first one is based on a necessary and sufficient condition whereas the second one is based on a sufficient (but simpler) condition only. Both certificates are obtained from any feasible solution of a related semidefinite program and so in principle, can be… CONTINUE READING

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