Distributionally Robust Geometric Joint Chance-Constrained Optimization: Neurodynamic Approaches
This work addresses optimization under uncertainty for applications like engineering and telecommunications, but it appears incremental as it adapts neural network methods to a specific problem type without broad new insights.
The paper tackles distributionally robust geometric joint chance-constrained optimization problems with unknown probability distributions by proposing a two-time scale neurodynamic duplex approach, which converges in probability to the global optimum without using standard state-of-the-art methods and is applied to shape optimization and telecommunication problems.
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.