We present an alternating augmented Lagrangian method for convex optimization
problems where the cost function is the sum of two terms, one that is separable
in the variable blocks, and a second that is separable in the difference
between consecutive variable blocks. Examples of such problems include Fused
Lasso estimation, total variation denoising, and multi-period portfolio
optimization with transaction costs. In each iteration of our method, the first
step involves separately optimizing over each variable block, which can be
carried out in parallel.
This paper addresses the problem of segmenting a time-series with respect to
changes in the mean value or in the variance. The first case is when the time
data is modeled as a sequence of independent and normal distributed random
variables with unknown, possibly changing, mean value but fixed variance. The
main assumption is that the mean value is piecewise constant in time, and the
task is to estimate the change times and the mean values within the segments.
The second case is when the mean value is constant, but the variance can
change.