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For optimization problems with linear equality constraints, we prove that the(1,1) block of the inverse KKT matrix remains unchanged when projected onto thenullspace of the constraint matrix. We develop reduced compact representationsof the limited-memory inverse BFGS Hessian to compute search directionsefficiently when the constraint Jacobian is sparse. Orthogonal projections areimplemented by a sparse QR factorization or a preconditioned LSQR iteration. Innumerical experiments two proposed trust-region algorithms improve incomputation times, often significantly, compared to previous implementations ofrelated algorithms and compared to IPOPT.

Large-scale Optimization with Linear Equality Constraints using Reduced Compact Representation