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:

- 1.
- Select
*q*variables*or*as the new working set, called . - 2.
- Fix the other variables to their current values and solve the problem (3) with respect to .
- 3.
- 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. - 4.
- 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.

- Selection of a New Working Set
- Solving the Subproblem
- Shrinking
- Termination Criterion
- Implementation Details
- Comparisons with Other Algorithms
- Convergence

Journal of Machine Learning Research