Certificates of convexity for basic semi-algebraic sets

✍ Scribed by J.B. Lasserre

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 266 KB
• Volume: 23
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2010.04.009

✦ Synopsis

We provide two certificates of convexity for arbitrary basic closed semi-algebraic sets of 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, in principle, can be obtained numerically (however, up to machine precision).