Distributionally Robust Geometric Joint Chance-Constrained Optimization: Neurodynamic Approaches

2026-02-10

AI Summary

This work proposes a two-timescale neural dynamical dual method for geometric joint chance-constrained optimization problems with unknown distributions belonging to a prescribed ambiguity set. For the first time, neural networks are integrated into distributionally robust chance-constrained optimization, enabling convergence to the global optimum almost surely without relying on conventional solvers and supporting parallel processing across multiple instances. By coupling projected equations with three canonical types of distributional ambiguity sets, the proposed framework demonstrates high efficiency and scalability in practical applications such as shape optimization and telecommunication network design, significantly enhancing both computational performance and problem applicability.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Computational social science

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.

Problem

• distributionally robust
• joint chance-constrained optimization
• geometric optimization
• uncertainty set
• probability distribution

Innovation

• distributionally robust optimization
• joint chance constraints
• neurodynamic approach
• projection equations
• geometric programming