6 papers
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…
On the Rate of Asymptotic Regularity of Iterative Methods for Nonexpansive Mappings in CAT(0) Spaces and Hyperbolic Optimization
Katherine Rossella Foglia, Vittorio Colao
The Krasnosel'ski\uı--Mann and Halpern iterations are classical schemes for approximating fixed points of nonexpansive mappings in Banach spaces, and have been widely studied in m…
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…
On the Convergence of HalpernSGD
Vittorio Colao, Katherine Rossella Foglia
We study a stochastic anchored gradient scheme, namely HalpernSGD, which combines the classical Halpern iteration for finding a minimizer of a convex and -smooth objective funct…
Limited-Memory LRSGA: An Iterative Method for Computing Nash Equilibria in Competitive Optimization Problems
Katherine Rossella Foglia, Francesco Sergio Pisani, Vittorio Colao
We introduce LMLRSGA, a limited memory variant of Low Rank Symplectic Gradient Adjustment (LRSGA) for differentiable games. It is an iterative scheme for approximating Nash equilib…
A Multi-Phase Dual-PINN Framework: Soft Boundary-Interior Specialization via Distance-Weighted Priors
Naseem Abbas, Vittorio Colao, Davide Macri +1
Physics-informed neural networks (PINNs) often struggle with multi-scale PDEs featuring sharp gradients and nontrivial boundary conditions, as the physics residual and boundary enf…