Convergence of a Newton algorithm for semi-discrete optimal transport
Copyright policy )Convergence of a Newton algorithm for semi-discrete optimal transport
A popular way to solve optimal transport problems numerically is to assume that the source probability measure is absolutely continuous while the target measure is finitely supported. We introduce a damped Newton algorithm in this setting, which is experimentally efficient, and we establish its global linear convergence for cost functions satisfying an assumption that appears in the regularity theory for optimal transport.
Computational Geometry (cs.CG), FOS: Computer and information sciences, 65K10, 49M25, Monge-Ampère equation, Numerical Analysis (math.NA), [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Analyse, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], 510, Laguerre diagram, Mathematics - Analysis of PDEs, optimal transport, [INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG], 49M25, 65K10, 515, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Computer Science - Computational Geometry, Mathematics - Numerical Analysis, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Analysis of PDEs (math.AP)
Computational Geometry (cs.CG), FOS: Computer and information sciences, 65K10, 49M25, Monge-Ampère equation, Numerical Analysis (math.NA), [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Analyse, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], 510, Laguerre diagram, Mathematics - Analysis of PDEs, optimal transport, [INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG], 49M25, 65K10, 515, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Computer Science - Computational Geometry, Mathematics - Numerical Analysis, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Analysis of PDEs (math.AP)
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