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Some Convergence Properties of Descent Methods

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  • Z. Wei
  • L. Qi
  • H. Jiang

Abstract

In this paper, we discuss the convergence properties of a class of descent algorithms for minimizing a continuously differentiable function f on R n without assuming that the sequence { x k } of iterates is bounded. Under mild conditions, we prove that the limit infimum of $$\left\| { \nabla f(x_k )} \right\|$$ is zero and that false convergence does not occur when f is convex. Furthermore, we discuss the convergence rate of { $$\left\| { x_k } \right\|$$ } and { f(x k )} when { x k } is unbounded and { f(x k )} is bounded.

Suggested Citation

  • Z. Wei & L. Qi & H. Jiang, 1997. "Some Convergence Properties of Descent Methods," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 177-188, October.
    • Handle: RePEc:spr:joptap:v:95:y:1997:i:1:d:10.1023_a:1022691513687
    DOI: 10.1023/A:1022691513687
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    1. Correa Romar, 2014. "Mathematical Foci," Mathematical Economics Letters, De Gruyter, vol. 2(1-2), pages 5-11, August.
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