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The Decomposition Algorithm

As in the classification algorithm proposed by Joachims [5], which was based on a idea from Osuna et al [11], our regression algorithm is subdivided into the following four steps, which are explained afterward in the following subsections:

Select q variables $\alpha_i$ or $\alpha_i^{\star}$ as the new working set, called $\mathcal{S}$.
Fix the other variables $\mathcal{F}$ to their current values and solve the problem (3) with respect to $\mathcal{S}$.
Search for variables whose values have been at 0 or C for a long time and that will probably not change anymore. This optional step is the shrinking phase, as these variables are removed from the problem.
Test whether the optimization is finished; if not, return to the first step.

Many other decomposition algorithms for regression have been published recently, and a comparison is given later in section 2.6.


Journal of Machine Learning Research