. Author manuscript; available in PMC: 2023 Dec 5.

Published in final edited form as: Phys Med Biol. 2022 Sep 12;67(18):10.1088/1361-6560/ac8044. doi: 10.1088/1361-6560/ac8044

Table 2.

The cost functions for each dose mimicking model that minimize mean absolute (MeanAbs), max absolute (MaxAbs), mean relative (MeanRel), and max relative (MaxRel) differences between all pairs of the optimized and predicted objective values $(g_{m} (w), {\hat{g}}_{m})$ .

	Dose mimicking model cost function
MeanAbs	$\underset{m \in M_{p}}{mean} {(g_{m} (w) - {\hat{g}}_{m})}^{+} + ϵ \underset{m \in M_{p}}{mean} {(g_{m} (w) - {\hat{g}}_{m})}^{-}$
MaxAbs	$\max_{m \in M_{p}} (g_{m} (w) - {\hat{g}}_{m})$
MeanRel	$\underset{m \in M_{p}}{mean} {(\frac{g_{m} (w) - {\hat{g}}_{m}}{{\hat{g}}_{m}})}^{+} + ϵ \underset{m \in M_{p}}{mean} {(\frac{g_{m} (w) - {\hat{g}}_{m}}{{\hat{g}}_{m}})}^{-}$
MaxRel	$\max_{m \in M_{p}} (\frac{g_{m} (w) - {\hat{g}}_{m}}{{\hat{g}}_{m}})$