Cyclic coordinate descent in a class of bang-singular-bang problems

with zi ∈ { Ĉ[0, T ] |zi(0) = 0, zi(T ) = bi } , with technical constraints for the consumption rate over time: mi ≤ żi(t) ≤Mi, ∀i = 1, . . . , n. We abstract from this situation to tackle a general problem which studies a production process whose efficiency of production with respect to each input depends on time, on the stock of the various inputs, and on the consumption rate of other inputs. The main limitation will be the linearity of the functional with respect to consumption rates and stocks, which will imply that it is a bang-singular-bang optimal control problem. We propose an efficient method for finding the bang-singular-bang solution using a cyclic coordinate descent strategy combined with a suitable adaptation of the shooting method