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We introduce the geodesic walk for sampling Riemannian manifolds and apply it to the problem of generating uniform random points from polytopes in R^n specified by m inequalities.
Efficient Monte-Carlo procedures for generating points uniformly distributed over bounded regions
R.L. Smith · 1984
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Brownian motion and stochastic flow systems
J. Michael Harrison · 1985
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A random polynomial time algorithm for approximating the volume of convex bodies
M. E. Dyer, A. M. Frieze, and R. Kannan · 1989
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Riemannian geometry underlying interior-point methods for linear programming
Narendra Karmarkar · 1990
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How to compute the volume?
L. Lovász · 1990
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Mixing rate of Markov chains, an isoperimetric inequality, and computing the volume
L. Lovász and M. Simonovits · 1990
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Computing the volume of a convex body: a case where randomness provably helps
M. E. Dyer and A. M. Frieze · 1991
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A random polynomial-time algorithm for approximating the volume of convex bodies
M. E. Dyer, A. M. Frieze, and R. Kannan · 1991
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On the randomized complexity of volume and diameter
L. Lovász and M. Simonovits · 1992
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Random walks in a convex body and an improved volume algorithm
L. Lovász and M. Simonovits · 1993
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Interior-point polynomial algorithms in convex programming
Yurii Nesterov, Arkadii Nemirovskii, and Yinyu Ye · 1994
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Fast algorithms for polynomial interpolation, integration, and differentiation
A Dutt, M Gu, and V Rokhlin · 1996
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Random walks and an O ∗ ( n 5 ) O^{*}(n^{5}) volume algorithm for convex bodies
R. Kannan, L. Lovász, and M. Simonovits · 1997
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Hit-and-run mixes fast
L. Lovász · 1998
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On the riemannian geometry defined by self-concordant barriers and interior-point methods
Yurii E Nesterov, Michael J Todd, et al · 2002
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The curvature of a hessian metric
Burt Totaro · 2004
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Geometric random walks: A survey
S. Vempala · 2005
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Fast algorithms for logconcave functions: sampling, rounding, integration and optimization
L. Lovász and S. Vempala · 2006
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A visual introduction to riemannian curvatures and some discrete generalizations
Yann Ollivier · 2013
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The entropic barrier: a simple and optimal universal self-concordant barrier
Sébastien Bubeck and Ronen Eldan · 2014
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A cubic algorithm for computing Gaussian volume
B. Cousins and S. Vempala · 2014
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Theoretical guarantees for approximate sampling from smooth and log-concave densities
Arnak S Dalalyan · 2014
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Canonical barriers on convex cones
Roland Hildebrand · 2014
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L. Lovász and S. Vempala · 2006
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Efficient inverse maintenance and faster algorithms for linear programming
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A faster cutting plane method and its implications for combinatorial and convex optimization
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On a natural dynamics for linear programming
Damian Straszak and Nisheeth K Vishnoi · 2015
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Rapid mixing of geodesic walks on manifolds with positive curvature
Oren Mangoubi and Aaron Smith · 2016
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Randomized interior point methods for sampling and optimization
Hariharan Narayanan · 2016
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