Bad projections of the PSD cone-Reference-Cited by-同舟云学术

Bad projections of the PSD cone

Published:2021-03-29 Issue:2 Volume:72 Page:261-280
ISSN:0010-0757
Container-title:Collectanea Mathematica
language:en
Short-container-title:Collect. Math.

Author:

Jiang Yuhan,Sturmfels Bernd^ORCID

Abstract

AbstractThe image of the cone of positive semidefinite matrices under a linear map is a convex cone. Pataki characterized the set of linear maps for which that image is not closed. The Zariski closure of this set is a hypersurface in the Grassmannian. Its components are the coisotropic hypersurfaces of symmetric determinantal varieties. We develop the convex algebraic geometry of such bad projections, with focus on explicit computations.

Funder

Max Planck Institute for Mathematics in the Sciences

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s13348-021-00319-4.pdf

Reference22 articles.

1. Blekherman, G., Parrilo, P., Thomas, R.: Semidefinite Optimization and Convex Algebraic Geometry, MOS-SIAM Series on Optimization 13. SIAM, Philadelphia (2012)

2. Cifuentes, D., Harris, C., Sturmfels, B.: The geometry of SDP-exactness in quadratic optimization. Math. Program. Ser. A 182, 399–428 (2020)

3. Cifuentes, D., Kahle, T., Parrilo, P.: Sums of squares in Macaulay2. J. Softw. Algebra Geometry 10, 17–24 (2020)

4. Collins, G.E.: Quantifier elimination for real closed fields by cylindrical algebraic decompostion. Springer Lecture Notes Comput. Sci. 33, 134–183 (1975)

5. Fawzi, H., Safey El Din, M.: A lower bound on the positive semidefinite rank of convex bodies. SIAM Journal on Applied Algebra and Geometry 2, 126–139 (2018)

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