What is inexact steepest descent method

Question

Is there anybody knowing what is the inexact steepest descent method for solving non-linear optimization problems? Any reference or formal definition available online? I was asked by someone, but didn't find the best answer. I think it should be an variation of the steepest descent method, but not sure.

Hope to get some ideas..

Thank you!

Answer 1

In this method are admitted relative errors on the search directions, more precisely, an approximation of the exact search direction is computed at each iteration.

^{arXiv:1207.0775 [math.OC]}

(Also) see Fliege and Fux Svaiter: "Steepest Descent Methods for Multicriteria Optimization" (PDF).