### A Schur-Complement Method for Sparse Quadratic Programming

In applying active-set methods to sparse quadratic programs, it is desirable
to utilize existing sparse-matrix techniques. We describe a quadratic
programming method based on the classical Schur complement. Its key feature
is that much of the linear algebraic work associated with an entire sequence
of iterations involves a *fixed* sparse factorization. Updates are
performed at every iteration to the factorization of a smaller matrix, which
may be treated as dense or sparse.

The use of a fixed sparse factorization allows an ``off-the shelf'' sparse
equation solver to be used repeatedly. This feature is ideally suited to
problems with structure that can be exploited by a specialized factorization.
Moreover, improvements in efficiency derived from exploiting new parallel and
vector computer architectures are immediately applicable.

An obvious application of the method is in sequential quadratic programming
methods for nonlinearly constrained optimization, which require solution of a
sequence of closely related quadratic programming subproblems. We discuss
some ways in which the known relationship between successive problems can be
exploited.

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