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We present algorithmic, complexity, and implementation results on the problem of sampling points from a spectrahedron, that is the feasible region of a semidefinite program.
The fundamental theorem of algebra in terms of computational complexity
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Randomized algorithms for robust control analysis and synthesis have polynomial complexity
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Random walks and an O ∗ ( n 5 ) {O}^{*}(n^{5}) volume algorithm for convex bodies
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Perturbation theory for homogeneous polynomial eigenvalue problems
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Simulated annealing in convex bodies and an O ∗ ( n 4 ) {O}^{*}(n^{4}) volume algorithm
L. Lovász and S. Vempala · 2003
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Implementation and evaluation of sdpa 6.0
M. Yamashita, K. Fujisawa, and M. Kojima · 2003
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Random walks for probabilistic robustness
G. Calafiore · 2004
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The polynomial eigenvalue problem
M. Berhanu · 2005
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On the complexity of computing determinants
E. Kaltofen and G. Villard · 2005
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S. Tabachnikov · 2005
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J.-D. Boissonnat and M. Teillaud · 2006
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A. T. Kalai and S. Vempala · 2006
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Fast algorithms for logconcave functions: Sampling, rounding, integration and optimization
Bypassing KLS: Gaussian cooling and an O ∗ ( n 3 ) {O}^{*}(n^{3}) volume algorithm
B. Cousins and S. Vempala · 2015
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A practical volume algorithm
B. Cousins and S. Vempala · 2016
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Nearly optimal refinement of real roots of a univariate polynomial
V. Y. Pan and E. P. Tsigaridas · 2016
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A conceptual introduction to Hamiltonian Monte Carlo
M. Betancourt · 2017
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Vaidya walk: A sampling algorithm based on the volumetric barrier
Y. Chen, R. Dwivedi, M. J. Wainwright, and B. Yu · 2017
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Hamiltonian Monte Carlo with boundary reflections, and application to polytope volume calculations
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The D-decomposition technique for linear matrix inequalities
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Approximate volume and integration for basic semialgebraic sets
D. Henrion, J. B. Lasserre, and C. Savorgnan · 2009
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A randomized cutting plane method with probabilistic geometric convergence
F. Dabbene, P. Shcherbakov, and B. T. Polyak · 2010
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Nonlinear computational geometry
I. Emiris, F. Sottile, and T. Theobald, editors · 2010
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Eigen v3, 2010
G. Guennebaud, B. Jacob, et al · 2010
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A. Chevallier, S. Pion, and F. Cazals · 2018
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Convergence rates of moment-sum-of-squares hierarchies for volume approximation of semialgebraic sets
M. Korda and D. Henrion · 2018
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Algorithmic theory of odes and sampling from well-conditioned logconcave densities, 2018
Y. T. Lee, Z. Song, and S. S. Vempala · 2018
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Convergence Rate of Riemannian Hamiltonian Monte Carlo and Faster Polytope Volume Computation
Y. T. Lee and S. Vempala · 2018
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The polynomial eigenvalue problem is well conditioned for random inputs
D. Armentano and C. Beltrán · 2019
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The real polynomial eigenvalue problem is well conditioned on the average
C. Beltrán and K. Kozhasov · 2019
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Random spectrahedra
P. Breiding, K. Kozhasov, and A. Lerario · 2019
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Practical volume estimation by a new annealing schedule for cooling convex bodies
A. Chalkis, I. Z. Emiris, and V. Fisikopoulos · 2019
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Separation bounds for polynomial systems
I. Z. Emiris, B. Mourrain, and E. Tsigaridas · 2019
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Computing the volume of compact semi-algebraic sets
P. Lairez, M. Mezzarobba, and M. Safey El Din · 2019
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On the complexity of the Lickteig–Roy subresultant algorithm
G. Lecerf · 2019
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Faster polytope rounding, sampling, and volume computation via a sub-linear ball walk
O. Mangoubi and N. K. Vishnoi · 2019
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Sampling the feasible sets of SDPs and volume approximation
A. Chalkis, V. Fisikopoulos, P. Repouskos, and E. Tsigaridas · 2020
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A header-only C++ library for large scale eigenvalue problems
Spectra · 2020
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