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SIAM J. Optim. 21, pp. 960-976 (17 pages)
Positive Polynomials and Projections of Spectrahedra
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Add to FacebookThis article is concerned with different aspects of spectrahedra and their projections, sets that are important in semidefinite optimization. We prove results on the limitations of so-called Lasserre and theta body relaxation methods for semialgebraic sets and varieties. As a special case we obtain the main result of Netzer, Plaumann, and Schweighofer [SIAM J. Optim., 20 (2010), pp. 1944–1955] on nonexposed faces. We also solve the open problems from that work. We further give a unified account of several results on convex hulls of curves and images of polynomial maps. We finally prove a Positivstellensatz for projections of spectrahedra, which exceeds the known results that only work for basic closed semialgebraic sets.
© 2011 Society for Industrial and Applied Mathematics
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Received July 12, 2010
Accepted June 17, 2011
Published online September 22, 2011
Accepted June 17, 2011
Published online September 22, 2011
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