English

Certificates of convexity for basic semi-algebraic sets

Optimization and Control 2010-01-30 v2

Abstract

We provide two certificates of convexity for arbitrary basic semi-algebraic sets of Rn\R^n. 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 can be obtained numerically (however, up to machine precision).

Cite

@article{arxiv.0901.4497,
  title  = {Certificates of convexity for basic semi-algebraic sets},
  author = {Jean B. Lasserre},
  journal= {arXiv preprint arXiv:0901.4497},
  year   = {2010}
}

Comments

6 pages; To appear in Applied Mathematics Letters

R2 v1 2026-06-21T12:05:35.558Z