6 papers
Uniform-in-time propagation of chaos for Second-Order Consensus-Based Optimization
Seung-Yeal Ha, Franca Hoffmann, Dohyeon Kim
We study second-order Consensus-Based Optimization (CBO), a derivative-free global optimization algorithm in which the consensus force and the multiplicative exploratory noise act…
Knothe-Rosenblatt maps via soft-constrained optimal transport
Ricardo Baptista, Franca Hoffmann, Minh Van Hoang Nguyen +1
In the theory of optimal transport, the Knothe-Rosenblatt (KR) rearrangement provides an explicit construction to map between two probability measures by building one-dimensional t…
Monotone Multispecies Flows
Lauren Conger, Franca Hoffmann, Eric Mazumdar +1
We present a novel notion of -monotonicity for an -species system of partial differential equations governed by mass-preserving flow dynamics, extending monotonicity in Bana…
Convex Constrained Controller Synthesis for Evolution Equations
Lauren Conger, Antoine P. Leeman, Franca Hoffmann
We propose a convex controller synthesis framework for a large class of constrained linear systems, including those described by (deterministic and stochastic) partial differential…
Computing Optimal Transport Plans via Min-Max Gradient Flows
Lauren Conger, Franca Hoffmann, Ricardo Baptista +1
We pose the Kantorovich optimal transport problem as a min-max problem with a Nash equilibrium that can be obtained dynamically via a two-player game, providing a framework for app…
Coupled Wasserstein Gradient Flows for Min-Max and Cooperative Games
Lauren Conger, Franca Hoffmann, Eric Mazumdar +1
We propose a framework for two-player infinite-dimensional games with cooperative or competitive structure. These games take the form of coupled partial differential equations in w…