“…It could be the maximization of the radiation dose delivered in an area V of a body for a cancer treatment problem, in which case one would take max Oϕ = ∆V −1 D(E)ϕ(r, E, Ω)drdEdΩ for r ∈ V, with D(E) being the flux-to-dose conversion function and ∆V the volume of area V. The optimization problem min/max Oϕ is subject to some constraints, denoted C(ρ, χ, ϕ(ρ, χ)) = 0, the first one being the requirement that the particle transport obeys the Boltzmann equation, and the other ones being additional constraints, for example, a limitation over the maximum quantity of matter available (weight constraint), or a constraint over the k eff of the system. This formalism is further discussed in Section 1 of [9].…”