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On the convergence of derivative-free methods for unconstrained optimization. (English) Zbl 1042.90617
Buhmann, Martin D. (ed.) et al., Approximation theory and optimization. Tributes to M. J. D. Powell on the occasion of his 60th birthday. Cambridge: Cambridge University Press (ISBN 0-521-58190-7/hbk). 83-108 (1997).
The authors consider the following problem: $$\min_{x\in\mathbb{R}^n}\,f(x)$$, where $$f$$ is smooth and such that $$\nabla f(x)$$ cannot be computed for any $$x$$. They derive a general framework in which reasonable global convergence results can be obtained.
For the entire collection see [Zbl 1001.00074].

##### MSC:
 90C30 Nonlinear programming 65K05 Numerical mathematical programming methods