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UID:20260404T071521EDT-82997UP1lO@132.216.98.100
DTSTAMP:20260404T111521Z
DESCRIPTION:Dynamic Games and Applications Seminar\n\n \n\nSpeaker: Martino
  Bardi – University of Padova\, Italy \n\n\n\nAbstract: Global unconstrain
 ed optimization of a non-convex function f in Euclidean space is a classic
 al problem that is attracting considerable new attention in view of applic
 ations to the training of deep neural networks\, especially for highly non
 linear\, possibly non-smooth loss functions f in very high space dimension
 . We show a connection between this problem and a 'critical' eikonal-type 
 equation arising also in ergodic control. A solution v of the critical Ham
 ilton-Jacobi equation is built by a small discount approximation as well a
 s the long-time limit of an associated finite horizon optimal control prob
 lem. Then v is represented as the value function of a control problem with
  target\, whose optimal trajectories are driven by a differential inclusio
 n describing the gradient descent of v. Such trajectories are proved to co
 nverge to the set of minima of f\, and in some cases\, they are shown to r
 each such points in finite time.\n\nJoint work with Hicham Kouhkouh (arXiv
 :2202.02561).\n
DTSTART:20220929T150000Z
DTEND:20220929T160000Z
LOCATION:CA\, ZOOM
SUMMARY:An Eikonal Equation with Vanishing Lagrangian Arising in Global Opt
 imization
URL:https://www.mcgill.ca/cim/channels/event/eikonal-equation-vanishing-lag
 rangian-arising-global-optimization-351859
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