  For optimization problems with sparse linear equality constraints, we observe
that the (1,1) block of the inverse KKT matrix remains unchanged when projected
onto the nullspace of the constraints. We develop reduced compact
representations of the limited-memory BFGS Hessian to compute search directions
efficiently. Orthogonal projections are implemented by sparse QR factorization
or preconditioned LSQR iteration. In numerical experiments two proposed
trust-region algorithms improve in computation times, often significantly,
compared to previous implementations and compared to IPOPT.
