Without loss of generality, we assume j > k. The goal of the training procedure is to find a parameter vector w that yields a "ranking score" function w • Φ(x i j ), which minimizes the number of violations of pairwise rankings provided in the training set.
the ideal w would satisfy the condition w The problem is typically treated as a Support Vector Machine constraint optimization problem, and can be solved using the search technique described in Joachims (2002a).