A kernel distributionally robust chance-constrained optimization (DRCCP) method is proposed in this study based on the kernel ambiguity set. The kernel ambiguity set is established via the kernel mean embedding (KME) and the maximum mean discrepancy (MMD) between distributions. The proposed approach can be formulated as two different models. The first one is a mixed-integer model employing the indicator function for handling the joint chance constraint. The second one is a continuous optimization model using the Conditional Value-at-Risk (CVaR) approximation to approximate the indicator function. The proposed method is compared with the popular Wasserstein ambiguity set based approach. A numerical example and a nonlinear process optimization problem are studied to demonstrate its efficacy.

本研究提出了一种基于核模糊集的核分布鲁棒机会约束优化（DRCCP）方法。内核歧义集是通过内核均值嵌入 (KME) 和分布之间的最大均值差异 (MMD) 建立的。所提出的方法可以表述为两种不同的模型。第一个是混合整数模型，使用指示函数来处理联合机会约束。第二个是连续优化模型，使用条件风险值 (CVaR) 逼近来逼近指标函数。所提出的方法与流行的基于 Wasserstein 模糊集的方法进行了比较。研究了一个数值例子和一个非线性过程优化问题来证明它的有效性。