Certificates of convexity for basic semi-algebraic sets

2009/01/28 by Lasserre, Jean B.
#14P10 11E25 52A20 90C22 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.0901.4497

Abstract

We provide two certificates of convexity for arbitrary basic 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 can be obtained numerically (however, up to machine precision).

Related

• Convexity in semi-algebraic geometry and polynomial optimization
• Two-sided convexity testing with certificates
• Real Algebraic Geometry and its Applications
• Convex Hulls of Algebraic Sets
• Semidefinite representation for convex hulls of real algebraic curves