On Convergence of Minimization Methods: Attraction, Repulsion, and Selection

Y. Zhang, R. Tapia and L. Velazquez
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Y. Zhang: Rice University
R. Tapia: Rice University
L. Velazquez: Massachusetts Institute of Technology

Journal of Optimization Theory and Applications, 2000, vol. 107, issue 3, No 5, 529-546

Abstract: Abstract In this paper, we revisit the convergence properties of the iterationprocess xk+1=xk−α(xk)B(xk)−1∇f(xk)for minimizing a function f(x). After reviewing some classic results andintroducing the notion of strong attraction, we give necessary andsufficient conditions for a stationary point of f(x) to be a point of strongattraction for the iteration process. Not only this result gives a newalgorithmic interpretation to the classic Ostrowski theorem, but alsoprovides insight into the interesting phenomenon called selectiveminimization. We present also illustrative numerical examples for nonlinearleast squares problems.

Keywords: attraction; repulsion; selective minimization (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1026443131121

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