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.

翻译：对于线性平等限制稀少的优化问题,我们注意到,KKT矩阵反面的(1,1)块在被投放到限制的空格上时保持不变,我们开发了有限的模拟BFGS Hessian 的缩略图,以有效计算搜索方向,通过稀疏的QR因数化或附设的LSQR迭代来实施正向预测。在数字实验中,两个拟议的信任区域算法在计算时间上有所改进,与以往的执行和IPOPT相比,往往显著改善。