Some Convergence Properties of Descent Methods

Z. Wei, L. Qi and H. Jiang

Journal of Optimization Theory and Applications, 1997, vol. 95, issue 1, No 8, 177-188

Abstract: 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.

Keywords: Unconstrained differentiable minimization; descent methods; global convergence; rate of convergence (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022691513687

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