What is it about?
Algorithms for high dimensional sampling and volume estimation of the feasible region of a semidefinite program as known as spectahedron. Spectahedra are generalizations of polyhedra with non-linear boundary. We provide the first software that efficiently samples as well as approximates the volume of spectahedra in hudrends of dimensions.
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Why is it important?
Sampling from the feasible set of a semidefinite program paves the way for efficient randomized optimization algorithms. Additionally, spectahedral volume is a fundamental quantity connected to applications in optimization.
Perspectives
Writing this article was one step towards randomized algorithms for optimization problems. On our way we have realized the advantages and weaknesses of randomized approaches. Our open source code can be used from researchers to experiment as well as estimate for the first time volume of high-dimensional spectahedra.
Vissarion Fisikopoulos
National and Kapodistrian University of Athens
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This page is a summary of: Sampling the feasible sets of SDPs and volume approximation, ACM Communications in Computer Algebra, September 2020, ACM (Association for Computing Machinery),
DOI: 10.1145/3457341.3457349.
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