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Analysis and Optimal Design of Equilibria in the Vlasov-Poisson System
Alfio Borzì, Gennaro Infante, Giovanni Mascali +1
The optimal design of equilibrium particle distributions generated by external electric fields is investigated in the framework of stationary Maxwellian equilibria of the Vlasov-Po…
MultiLRSGA: A method for multi-player differentiable games
Katherine Rossella Foglia, Vittorio Colao, Alfio Borzì
We propose MultiLRSGA, an -player extension of LRSGA for the computation of stable Nash equilibria in differentiable games. The method originates from the decomposition of the g…
A Moser-Type Construction for the Liouville Equation
Alfio Borzì, Marco Caponigro, Arianna Vicari
A Moser-type construction for the kinetic Liouville equation is proposed, which is based on a characteristic-adapted interpolation. For Hamiltonian accelerations, the construction…
A Low-Rank Symplectic Gradient Adjustment Method for Computing Nash Equilibria
Nadja Vater, Katherine Rossella Foglia, Vittorio Colao +1
This work presents a theoretical and numerical investigation of the symplectic gradient adjustment (SGA) method and of a low-rank SGA (LRSGA) method for efficiently solving revviol…
Adjoint-based optimal control of jump-diffusion processes
Jan Bartsch, Alfio Borzi, Gabriele Ciaramella +1
Stochastic differential equations (SDEs) using jump-diffusion processes describe many natural phenomena at the microscopic level. Since they are commonly used to model economic and…
The Pontryagin Maximum Principle for Training Convolutional Neural Networks
Sebastian Hofmann, Alfio Borzì
A novel batch sequential quadratic Hamiltonian (bSQH) algorithm for training convolutional neural networks (CNNs) with -based regularization is presented. This methodology is…