Abstract
We discuss two issues related to the Cauchy algorithm. First, we use anArmijo search with constant α≥0.5 and show that the sequence isFejer convergent to the optimal set, and hence convergent. Second, we useexact line searches and show an example in which the sequence fails toconverge.
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Gonzaga, C.C. Two Facts on the Convergence of the Cauchy Algorithm. Journal of Optimization Theory and Applications 107, 591–600 (2000). https://doi.org/10.1023/A:1026451300170
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DOI: https://doi.org/10.1023/A:1026451300170