TABLE I.

List and description of variables involved with the column generation algorithm.

Variable	Type	Description
Tall	Set	Set of all available triplets
Tselect	Set	Set of selected triplets
t	Index	Index for triplet
s	Index	Index for OAR
r	Index	Index for PTV
m	Index m ∈ s, r	Index for structure. Includes both OAR and PTV structures
αm	Scalar	Weight for mth structure
$G_m\left(\cdot \right)$	Function	Cost function for mth structure
ft	Vector	Fluence of tth triplet. Single element of ft is referred to as “beamlet”
At	Matrix	Fluence-to-dose transformation matrix for tth triplet
d	Vector	Dose array containing all voxels in dose domain
dm	Vector	Dose array containing only voxels for mth structure
γs	Scalar 0 ≤ γs ≤ 1	Trade-off factor between mean dose and max dose for the sth OAR
pr	Vector	Prescription dose for rth PTV. Entire vector typically set to one value
u	Vector	Lagrange multiplier corresponding to the constraint d = ∑t∈TallAtft
v	Vector	Lagrange multiplier corresponding to the constraint d ≤ q
wt	Vector	Lagrange multiplier corresponding to the constraint ft ≥ 0 for t ∈ Tall