Differential Equations and Nonlinear Analysis Seminar: Jérôme Bolte, Université Toulouse 1 Capitole, A Bestiary of Counterexamples in Smooth Convex Optimization
ZoomCounterexamples to some old-standing optimization problems in the smooth convex coercive setting are provided. Block-coordinate, steepest descent with exact search or Bregman descent methods do not generally converge. Other failures of various desirable features are established: directional convergence of Cauchy’s gradient curves, convergence of Newton’s flow, finite length of Tikhonov path, convergence of central paths,…