000172406 001__ 172406
000172406 005__ 20181203022557.0
000172406 0247_ $$2doi$$a10.1007/s00211-010-0305-8
000172406 02470 $$2ISI$$a000281397600001
000172406 037__ $$aARTICLE
000172406 245__ $$aDerivatives with respect to metrics and applications: subgradient marching algorithm
000172406 269__ $$a2010
000172406 260__ $$c2010
000172406 336__ $$aJournal Articles
000172406 520__ $$aThis paper introduces a subgradient descent algorithm to compute a Riemannian metric that minimizes an energy involving geodesic distances. The heart of the method is the Subgradient Marching Algorithm to compute the derivative of the geodesic distance with respect to the metric. The geodesic distance being a concave function of the metric, this algorithm computes an element of the subgradient in O(N (2) log(N)) operations on a discrete grid of N points. It performs a front propagation that computes a subgradient of a discrete geodesic distance. We show applications to landscape modeling and to traffic congestion. Both applications require the maximization of geodesic distances under convex constraints, and are solved by subgradient descent computed with our Subgradient Marching. We also show application to the inversion of travel time tomography, where the recovered metric is the local minimum of a non-convex variational problem involving geodesic distances.
000172406 6531_ $$aHamilton-Jacobi Equations
000172406 6531_ $$aTravel-Time Tomography
000172406 6531_ $$aTraffic Congestion
000172406 6531_ $$aEquilibria
000172406 700__ $$aBenmansour, F.
000172406 700__ $$aCarlier, G.
000172406 700__ $$aPeyre, G.
000172406 700__ $$aSantambrogio, F.
000172406 773__ $$j116$$q357-381$$tNumerische Mathematik
000172406 909C0 $$0252087$$pCVLAB$$xU10659
000172406 909CO $$ooai:infoscience.tind.io:172406$$pIC$$particle
000172406 917Z8 $$x112366
000172406 937__ $$aEPFL-ARTICLE-172406
000172406 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED
000172406 980__ $$aARTICLE