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SUMMARY:Backward Step Control globalization for Newton-type methods: D
 r. Andreas Potschka (IWR Heidelberg)
UID:529aae46-28d7-4b5a-9974-a8d79eea2e02
DESCRIPTION:ABSTRACT: We present a step size selection method for the 
 globalization of convergence of Newton-type methods for nonlinear root
  finding problems and its generalization to a Hilbert space setting. T
 he approach generalizes on the well-known interpretation of the Newton
  method as an explicit Euler time-stepping scheme for the Davidenko di
 fferential equation to the setting of Newton-type directions that may 
 deviate from the exact Newton direction. The advantages of the globali
 zation strategy comprise a simple yet efficient implementation and a r
 igorous convergence analysis based on generalized Newton paths\, which
  are the solution to an inital value problem of an appropriate general
 ization of the Davidenko differential equation. Under reasonable assum
 ptions\, the results of the convergence analysis include full steps in
  the vicinity of a solution\, a uniform lower step size bound\, a prio
 ri guarantees for the nonlinear decrease of the residual norm\, and co
 nvergence to a distinguished root\, namely the end point of the genera
 lized Newton path emanating from the initial guess. In addition\, the 
 framework delivers suitable relative termination tolerances for inexac
 t residual minimizing Krylov&#8211\;Newton methods and can be utilized
  to derive general purpose adaptive grid refinement strategies for fin
 ite element discretizations of elliptic PDE problems. For optimization
  problems\, the idea of Backward Step Control can be applied within a 
 generic homotopy approach. We conclude the talk with numerical results
  for the unconstrained optimization problems of the CUTEst test set an
 d for the minimal surface PDE.
DTSTART:20171109T151500Z
DTEND:20171109T161500Z
LOCATION:H13
DTSTAMP:20260723T191125Z
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