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math.AP2026
The nonlocal attraction-repulsion transport equation with power kernels
Massimo Fornasier, Hui Huang, Lukang Sun
We study a nonlocal continuity equation on in which a probability density is driven by the competition between attraction toward a prescribed background measure …
math.AP2026
Large-Time Analysis of the Langevin Dynamics for Energies Fulfilling Polyak-Åojasiewicz Conditions
Massimo Fornasier, Lukang Sun, Rachel Ward
In this work, we take a step towards understanding overdamped Langevin dynamics for the minimization of a general class of objective functions . We establish well-pose…
math.AP2025
Regularity and positivity of solutions of the Consensus-Based Optimization equation: unconditional global convergence
Massimo Fornasier, Lukang Sun
Introduced in 2017 \cite{B1-pinnau2017consensus}, Consensus-Based Optimization (CBO) has rapidly emerged as a significant breakthrough in global optimization. This straightforward…