Distributionally Robust Geometric Joint Chance-Constrained Optimization: Neurodynamic Approaches

TL;DR

This paper introduces a neural network-based method for solving distributionally robust geometric joint chance-constrained optimization problems, ensuring convergence to the global optimum without traditional solvers.

Contribution

It presents a novel neurodynamic duplex approach that handles unknown distributional uncertainties and converges to the global solution.

Findings

Neural network approach converges in probability to the global optimum.

Method successfully applied to shape optimization and telecommunication problems.

Proposes three uncertainty sets for distributional robustness.

Abstract

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.