Speaker
Description
Solving PDE-constrained generalized Nash equilibrium problems (GNEPs) poses significant mathematical and computational challenges. Inspired by applications in gas markets, we study a GNEP where multiple agents seek to maximise their individual profit on a commodity transported through the network. The dynamics of the shared state variable, representing the commodity flow, are modeled using a viscosity-regularized transport equation on the network. Each agent controls this state through their individual strategies, which are subject to private constraints and unknown to other agents. Further, each agent must abide by shared state constraints, which are managed using Moreau-Yosida regularization. As the agents’ strategies and their constraints are unknown to each other, we propose a centralized, distributed approach to solving the GNEP. While the state is solved via a global operator who observes the actions of all agents, the adjoint-based computation of the individual updates to the strategies is distributed across the agents. This natural parallelization creates an exchange of information between the global and local levels, which allows for scalability and efficiency in solving large-scale optimization problems. In this talk, we will detail the proposed method and discuss its convergence properties. Numerical experiments will illustrate the algorithm’s performance, demonstrating its robustness and efficiency.
