A counterexample of the convergence of Rosen’s algorithm with inexact line search

Du and Zhang recently proved that Rosen’s gradient projection method converges when using either exact or Armijo-type inexact line searches. The paper shows here that the method fails to converge when the inexact line search proposed in the original paper is used. The same quadratic programming counterexample can be used to show that Ritter’s method with Rosen’s inexact line search also fails to converge.