Certificates of convexity for basic semi-algebraic sets

@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}
}
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