and then the filter is augmented to form the taboo region of the next iterate
 (29)
Otherwise,  is rejected and  . Then the new trial point is calculated and tested. This process is repeated until an acceptable  is found or  is less than  . If the latter happens, the algorithm gives up the line-search procedure and initiates the feasibility restore phase to compute a new acceptable iterate.
If the current μ-barrier problem is successfully solved to expected accuracy, the filter is reset to an empty set.
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