Extending the program to more general constraints

It is not difficult to include more general constraints in the above program. Imagine a constraint that the sum of the data points must be zero. This would be implemented by first seeing that the mean began at zero and then at each iteration removing the mean from the gradient. Then any amount of the gradient can added to the solution and the data would retain a zero mean. Other constraints could be handled likewise because the mean is merely an unweighted sum and the same idea applies to weighted sums. Thus multiple linear constraints can be handled, so long as there are not so many of them that they bog down the calculation.