### A Globally Convergent Stabilized SQP Method

Sequential quadratic programming (SQP) methods are a popular class of
methods for nonlinearly constrained optimization. They are particularly
effective for solving a sequence of related problems, such as those arising
in mixed-integer nonlinear programming and the optimization of functions
subject to differential equation constraints.

Recently, there has been considerable interest in the formulation of
* stabilized * SQP methods, which are specifically designed to handle
degenerate optimization problems. Existing stabilized SQP methods are
essentially local, in the sense that both the formulation and analysis
focus on the properties of the methods in a neighborhood of a solution. A
new SQP method is proposed that has favorable global convergence properties
yet, under suitable assumptions, is equivalent to a variant of the
conventional stabilized SQP method in the neighborhood of a solution. The
method combines a primal-dual generalized augmented Lagrangian function
with a flexible line search to obtain a sequence of improving estimates of
the solution. The method incorporates a convexification algorithm that
allows the use of exact second-derivatives to define a convex quadratic
programming (QP) subproblem without requiring that the Hessian of the
Lagrangian be positive definite in the neighborhood of a solution. This
gives the potential for fast convergence in the neighborhood of a solution.
Additional benefits of the method are that each QP subproblem is
regularized and the QP subproblem always has a known feasible point.
Numerical experiments are presented for a subset of the problems from
the CUTEr test collection.

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