### On the Performance of SQP Methods for Nonlinear Optimization

This paper concerns some practical issues associated with the
formulation of sequential quadratic programming (SQP) methods for
large-scale nonlinear optimization. SQP methods find an approximate
solution of a sequence of quadratic programming (QP) subproblems in which a
quadratic model of the objective function is minimized subject to the
linearized constraints. Extensive numerical results are given for 1153
problems from the CUTEst test collection. The results indicate that SQP
methods based on maintaining a quasi-Newton approximation to the Hessian of
the Lagrangian function are both reliable and efficient for general
large-scale optimization problems. In particular, the results show that in
some situations, quasi-Newton methods are more efficient than competing
methods based on the exact Hessian of the Lagrangian. The paper concludes
with discussion of an SQP method that employs both approximate and exact
Hessian information. In this approach the quadratic programming subproblem
is either the conventional subproblem defined in terms of a
positive-definite quasi-Newton approximate Hessian, or a convexified
problem based on the exact Hessian.

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