### Some Theoretical Properties of an Augmented Lagrangian Merit Function

Sequential quadratic programming (SQP) methods for
nonlinearly constrained optimization typically use a *merit function *
to enforce convergence from an arbitrary starting point. We
define a *smooth* augmented Lagrangian merit function in which
the Lagrange multiplier estimate is treated as a separate variable, and
inequality constraints are handled by means of non-negative slack
variables that are included in the linesearch. Global convergence is
proved for an SQP algorithm that uses this merit function. We also
prove that steps of unity are accepted in a neighborhood of the
solution when this merit function is used in a suitable superlinearly
convergent algorithm. Finally, some numerical results are presented
to illustrate the performance of the associated SQP method.

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