On Convergence of Minimization Methods: Attraction, Repulsion and Selection
In 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.
Citable link to this pagehttps://hdl.handle.net/1911/101917
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