Semi-discrete Flow Matching produces terminal assignment regions that are topologically simple (open, simply connected, homeomorphic to the ball under assumption) yet geometrically distinct from optimal transport Laguerre cells, as they can be non-convex with curved boundaries.
SIAM Journal on Optimization , volume=
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Establishes exponential convergence in Wasserstein distance for the mean-field limit and finite-particle approximation of a consensus-based method solving nonconvex bi-level optimization problems.
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Tessellations of Semi-Discrete Flow Matching
Semi-discrete Flow Matching produces terminal assignment regions that are topologically simple (open, simply connected, homeomorphic to the ball under assumption) yet geometrically distinct from optimal transport Laguerre cells, as they can be non-convex with curved boundaries.
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Convergence of Consensus-Based Particle Methods for Nonconvex Bi-Level Optimization
Establishes exponential convergence in Wasserstein distance for the mean-field limit and finite-particle approximation of a consensus-based method solving nonconvex bi-level optimization problems.
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