Certificates of convexity for basic semi-algebraic sets

Details Certificates of convexity for basic semi-algebraic sets Certificates of convexity for basic semi-algebraic sets

2009-01-28

arxiv.org/abs/0901.4497v2

Mathematics

Optimization and Control

6 pages; To appear in Applied Mathematics Letters

Scientific paper

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

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