The article develops a parametric model of fairness called "$\varepsilon$-fairness" that can be represented using a single second-order cone constraint and incorporated into existing decision-making problem formulations without impacting the complexity of solution techniques. We develop the model from the fundamental result of finite-dimensional norm equivalence in linear algebra and show that this model has a closed-form relationship to an existing metric for measuring fairness widely used in the literature. Finally, a simple case study on the optimal operation of a damaged power transmission network illustrates its effectiveness.

翻译：本文提出了一种称为“$\varepsilon$-公平性”的参数化公平性模型，该模型可通过单一二阶锥约束表示，并能融入现有决策问题公式中而不影响求解技术的复杂度。我们基于线性代数中有限维范数等价的基本结论构建该模型，并证明该模型与文献中广泛使用的现有公平性度量指标存在闭式关系。最后，通过受损输电网络最优运行的简单案例研究验证了其有效性。