Zhang, YinTapia, RichardVelazquez, Leticia2018-06-182018-06-181999-03Zhang, Yin, Tapia, Richard and Velazquez, Leticia. "On Convergence of Minimization Methods: Attraction, Repulsion and Selection." (1999) <a href="https://hdl.handle.net/1911/101917">https://hdl.handle.net/1911/101917</a>.https://hdl.handle.net/1911/101917In this paper, we introduce a rather straightforward but fundamental observation concerning the convergence of the general iteration process. x^(k+1) = x^k - alpha(x^k) [B(x^k)]^(-1) grad­f(x^k) for minimizing a function f(x). We give necessary and sufficient conditions for a stationary point of f(x) to be a point of strong attraction of the iteration process. We will discuss various ramifications of this fundamental result, particularly for nonlinear least squares problems.18 ppengTechnical reportTR99-12