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[S] termination criterion citation sought

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Subject: [S] termination criterion citation sought
From: Bruce McCullough <BMCCULLO@fcc.gov>
Date: Wed, 19 Aug 1998 14:50:01 -0400
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I am presently reading about stopping rules for
nonlinear iterative solvers, in particular uncontstrained
minimization and unconstrained least squares.

Some time ago I stumbled across a "good" criterion
which, the author wrote, was _not_ in Gill, Murray
and Wright.  I can't for the life of me remember the
reference.  Can anyone help?

More generally, I am concerned with why a nonlinear
solver will incorrectly report having found a "solution". 
That is, the iterations converge to a point which is
not a solution, and the solver fails to recognize that the
point in question is not a solution.

Many thanks,

Bruce

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