## Large Sparse Numerical Optimization |

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### Contents

Large Sparse Systems of Linear Equations | 1 |

Large Sparse Linear Least Squares | 26 |

Large Sparse Linear Programming | 35 |

Copyright | |

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### Common terms and phrases

adjacency graph applied approach approximation assume bandwidth BFGS update bipartite graph block Cholesky decomposition Cholesky factor coloring of GS(A Computer Science conjugate gradient method constraints defined described in Section determined diagonal direct method discussed dogleg edges Edited efficient equivalent example Hence Hessian matrix heuristic implementation iteration Jacobian large sparse setting least squares problem linear least squares linear programming linear system lower triangular minimize MINPACK-1 Newton Newton's method node nonlinear least squares Note number of nonzeroes Numerical Analysis optimization problem ordering orthogonal partition permutation matrix pivoting positive definite positive semi-definite possible Powell and Toint QR decomposition quadratic quasi-Newton method rithm rows and columns satisfies Saunders scheme simplex method solved sparse Broyden update sparse linear sparse matrix sparse problems step steplength storage structure superlinear convergence symmetric matrix techniques Theorem tion triangular substitution method trust region upper triangular form vector vertex zero