Complexity Analysis of a Sampling-Based Interior Point Method for Convex Optimization
Keyword(s):
We develop a short-step interior point method to optimize a linear function over a convex body assuming that one only knows a membership oracle for this body. The approach is based a sketch of a universal interior point method using the so-called entropic barrier. It is well known that the gradient and Hessian of the entropic barrier can be approximated by sampling from Boltzmann-Gibbs distributions and the entropic barrier was shown to be self-concordant. The analysis of our algorithm uses properties of the entropic barrier, mixing times for hit-and-run random walks, approximation quality guarantees for the mean and covariance of a log-concave distribution, and results on inexact Newton-type methods.
2014 ◽
Vol 166
(2)
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pp. 572-587
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2017 ◽
Vol 174
(2)
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pp. 636-638
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2014 ◽
Vol 166
(2)
◽
pp. 588-604
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Keyword(s):
2016 ◽
Vol 73
(1)
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pp. 27-42
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Keyword(s):
2017 ◽
Vol 10
(04)
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pp. 1750070
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2014 ◽
Vol 276
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pp. 589-611
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