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Some Convergence Properties of Descent Methods

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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.

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Authors
  1. Z. Wei
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  2. L. Qi
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  3. H. Jiang
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Wei, Z., Qi, L. & Jiang, H. Some Convergence Properties of Descent Methods. Journal of Optimization Theory and Applications 95, 177–188 (1997). https://doi.org/10.1023/A:1022691513687

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  • DOI: https://doi.org/10.1023/A:1022691513687

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