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Examples of non-convergence of conjugate descent algorithms with exact line-searches (1977)

Thompson, J. R.

Springer

Mathematical programming 12 (1977), S. 356-360

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ISSN: 1436-4646

Keywords: Conjugate ; Convergence ; Exact Line-search ; Optimization

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: Abstract Examples are given in which quasi-Newton and other conjugate descent algorithms fail to converge to a minimum of the object function. In the first there is convergence to a point where the gradient is infinite; in the second, a region characterized by a fine terraced structure causes the iterates to spiral indefinitely. A modification of the second construction gives convergence to a point where the gradient is non-zero, but the gradient is not continuous at this point. The implication of these examples is discussed.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01593803

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