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Interior Point Methods in Machine Learning

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Technical Report ERGO-10-004

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J. Gondzio
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Abstract
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Interior point methods for linear and (convex) quadratic programming
display several features which make them particularly attractive for
very large scale optimization. They have an impressive low-degree
polynomial worst-case complexity. In practice, they display an unrivalled
ability to deliver optimal solutions in an almost constant number
of iterations which depends very little, if at all, on the problem
dimension. Since many problems in machine learning can be recast
as linear or quadratic optimization problems and it is common
for them to have large or huge sizes, interior point methods are
natural candidates to be applied in this context.
In this chapter we will discuss several major issues related to interior
point methods including the worst-case complexity result,
the features responsible for their ability to solve very large problems,
and their existing and potential applications in machine learning.

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Key words:
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Interior Point Methods, Machine Learning,
Quadratic Programming, Matrix-Free Methods.

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Text
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PDF ERGO-10-004.pdf.

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History:
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Written: July 23, 2010, revised September 28, 2010.

To appear as a chapter in the book:

S. Sra, S. Nowozin and S. Wright (eds),
**Optimization for Machine Learning**.
MIT Press, 2010.