Certificates of convexity for basic semi-algebraic sets

We provide two certificates of convexity for arbitrary basic closed semi-algebraic sets of Rn. 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).

• Type: Journal
• Year: 2010
• Where: APPML
• Authors: Jean B. Lasserre
• Keywords: APPML 2010, Arbitrary Basic, Semi-algebraic Sets, Sufficient Condition