This paper proposes a two-time scale neurodynamic duplex approach to solve distributionally robust geometric joint chance-constrained optimization problems. The probability distributions of the row vectors are not known in advance and belong to a certain distributional uncertainty set. In our paper, we study three uncertainty sets for the unknown distributions. The neurodynamic duplex is designed based on three projection equations. The main contribution of our work is to propose a neural network-based method to solve distributionally robust joint chance-constrained optimization problems that converges in probability to the global optimum without the use of standard state-of-the-art solving methods. We show that neural networks can be used to solve multiple instances of a problem. In the numerical experiments, we apply the proposed approach to solve a problem of shape optimisation and a telecommunication problem.

翻译：本文提出一种双时间尺度神经动力学对偶方法，用于求解分布鲁棒几何联合机会约束优化问题。行向量的概率分布并非预先已知，且属于特定的分布不确定性集合。本文针对未知分布研究了三种不确定性集合。神经动力学对偶系统基于三个投影方程设计而成。本研究的主要贡献在于提出一种基于神经网络的方法来求解分布鲁棒联合机会约束优化问题，该方法能以概率收敛至全局最优解，且无需依赖标准的先进求解方法。我们证明了神经网络可用于求解问题的多个实例。在数值实验中，我们将所提方法应用于形状优化问题与通信问题的求解。