Posts Tagged ‘optimization’

Linear Addition from the Log Domain

February 24, 2013

Some speech recognizers and machine learning algorithms need to quickly calculate the quantity:

\log(x+y)

when given only \log(x) and \log(y). The straightforward algorithm first uses the exponential function to convert the log values to the linear domain representation x and y, then performs the sum, and finally uses the log function to convert back to the log domain:

\log(x+y) = \log(\exp(\log(x)) + \exp(\log(y)))

These conversions between log and linear domains are slow and problems arise when x is too large or small for a machine’s floating point representation.

Luckily, there is a clever approximation method that allows quick, accurate calculation with a relatively small precomputed table.

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Second Order Cone Programming with CVXOPT

December 18, 2010

CVXOPT is a convex optimization package for Python that includes a Second Order Cone Programming (SOCP) solver.  The SOCP solver takes a set of matrices that describe the SOCP problem, but these matrices are different than the matrices usually used to express the SOCP problem.  This post walks through the simple algebra steps to find relationship between the two formulations of the SOCP problem.

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