# The Azimuth Project Co-ordinate descent (changes)

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## Idea

Co-ordinate descent is a technique for optimizing a multivariate function by simply repeatedly optimizing along each co-ordinate axis in turn. Although this is a less “intelligent” choice than utilising the gradient direction, it sometimes turns out allow closed form optimisations in that direction, resulting in being overall faster. A case where co-ordinate descent is often used is in sparse regression, wherepart of the function being optimized is oriented along the co-ordinate axes (eg, $L_1$ regression has $\sum_i |x_i|$, the sum of the absolute values of each of the variables.)