When performing constrained optimization on a smooth, convex function using coordinate descent, for what types of constraints will the algorithm work ? (i.e. converge or reach an approximate optimum within a tolerance of the constraint)
My understanding is that coordinate descent will work for
- Box constraints: e.g. $x_1 leq -1$ and $x_2 leq -1$
- Linear constraints: e.g. $x_2 leq -x_1 -1$
- Any others ?
In other words, how can we know whether or not coordinate descent can be applied to a contrained optimization problem ?
PS: irrespective of whether this is the right algorithm to use