Journal
APPLIED MATHEMATICS LETTERS
Volume 23, Issue 8, Pages 912-916Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.aml.2010.04.009
Keywords
Computational geometry; Basic semi-algebraic sets; Convexity; Semidefinite programming
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Funding
- (French) ANR [NT05-3-41612]
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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). (c) 2010 Elsevier Ltd. All rights reserved.
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