  We propose a data aggregation-based algorithm with monotonic convergence to a
global optimum for a generalized version of the L1-norm error fitting model
with an assumption of the fitting function. The proposed algorithm generalizes
the recent algorithm in the literature, aggregate and iterative disaggregate
(AID), which selectively solves three specific L1-norm error fitting problems.
With the proposed algorithm, any L1-norm error fitting model can be solved
optimally if it follows the form of the L1-norm error fitting problem and if
the fitting function satisfies the assumption. The proposed algorithm can also
solve multi-dimensional fitting problems with arbitrary constraints on the
fitting coefficients matrix. The generalized problem includes popular models
such as regression and the orthogonal Procrustes problem. The results of the
computational experiment show that the proposed algorithms are faster than the
state-of-the-art benchmarks for L1-norm regression subset selection and L1-norm
regression over a sphere. Further, the relative performance of the proposed
algorithm improves as data size increases.
