Certificates of convexity for basic semi-algebraic sets
Jean B. Lasserre (LAAS)

TL;DR
This paper introduces two numerical certificates to verify the convexity of basic semi-algebraic sets in real space, one exact and one sufficient, both derived from semidefinite programming solutions.
Contribution
It presents novel certificates for convexity of semi-algebraic sets, applicable via semidefinite programming, enhancing computational verification methods.
Findings
Certificates are derived from feasible solutions of semidefinite programs.
One certificate provides a necessary and sufficient condition.
The other offers a simpler sufficient condition.
Abstract
We provide two certificates of convexity for arbitrary basic semi-algebraic sets of . 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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Taxonomy
TopicsAdvanced Optimization Algorithms Research · Optimization and Variational Analysis · Point processes and geometric inequalities
