This paper first studies an expected utility problem with chance constraints and incomplete information on a decision maker’s utility function. The model maximizes the worst-case expected utility of random outcome over a set of concave functions within a novel ambiguity set, while the underlying probability distribution is known with the assumption of a discretization of possible realizations for the uncertainty parameter. To obtain computationally tractable formulations, we employ a discretization approach to derive a max–min chance-constrained approximation of this problem. This approximation is further reformulated as a mixed-integer program. We show that the discrete approximation converges to the true counterpart under mild assumptions. We also present a row generation algorithm for optimizing the max–min program. A computational study for a bin-packing problem and a multi-item newsvendor problem is conducted to demonstrate the benefit of the proposed framework and the computational efficiency of our algorithm. We find that the row generation algorithm can significantly reduce the computational time, and our robust policy could achieve a better out-of-sample performance when compared with the non-robust policy and the one without the chance constraints.

中文翻译：

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在机会约束下实现稳健的凹面效用最大化


本文首先研究了一个具有机会约束和决策者效用函数信息不完整的预期效用问题。该模型在新颖的模糊性集中的一组凹函数上最大化了随机结果的最坏情况预期效用，而潜在的概率分布是已知的，假设不确定性参数的可能实现是离散化的。为了获得计算上可处理的公式，我们采用离散化方法来推导出这个问题的最大-最小机会约束近似值。此近似值进一步重新表述为混合整数程序。我们表明，在温和的假设下，离散近似会收敛到真实的对应物。我们还提出了一种用于优化 max-min 程序的行生成算法。对 bin-packing 问题和多项目 newsvendor 问题进行了计算研究，以证明所提出的框架的好处和我们算法的计算效率。我们发现行生成算法可以显著减少计算时间，与非稳健策略和没有机会约束的策略相比，我们的稳健策略可以实现更好的样本外性能。