$\Gamma$-maximin, $\Gamma$-maximax and inteval dominance are familiar decision criteria for making decisions under severe uncertainty, when probability distributions can only be partially identified. One can apply these three criteria by solving sequences of linear programs. In this study, we present new algorithms for these criteria and compare their performance to existing standard algorithms. Specifically, we use efficient ways, based on previous work, to find common initial feasible points for these algorithms. Exploiting these initial feasible points, we develop early stopping criteria to determine whether gambles are either $\Gamma$-maximin, $\Gamma$-maximax or interval dominant. We observe that the primal-dual interior point method benefits considerably from these improvements. In our simulation, we find that our proposed algorithms outperform the standard algorithms when the size of the domain of lower previsions is less or equal to the sizes of decisions and outcomes. However, our proposed algorithms do not outperform the standard algorithms in the case that the size of the domain of lower previsions is much larger than the sizes of decisions and outcomes.

翻译：$Gamma $- maxim、 $\Gamma$- meximax 和 Inteval max- max and inval max macess 是在严重不确定性下作出决定的熟悉决策标准, 而概率分布只能部分确定。 您可以通过解析线性程序序列来应用这三项标准。 在本研究中, 我们为这些标准提出新的算法, 并将其性能与现有的标准算法进行比较。 具体地说, 我们根据先前的工作, 使用高效的方法为这些算法找到共同的初始可行点。 利用这些初步可行的点, 我们开发早期停止标准, 以确定赌博是否为$\Gamma $- meximin、 $\ gammam- masymaximax 或间距主导。 我们观察到, 初等内点方法大大受益于这些改进。 在我们的模拟中, 我们发现, 我们提议的算法在较低预视域的面积小于决定和结果大小大得多的情况下, 我们提议的算法超越了标准算法。