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References

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R. H. Bartels. A stabilization of the simplex method. Numerische Mathematik, 16:414–434, 1971.

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R. H. Bartels and G. H. Golub. The simplex method of linear programming using the lu decomposition. Communications of the ACM, 12:266–268, 1969.

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G. B. Dantzig. Linear programming and extensions. 1963.

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W. C. Davidon. Variable metric methods for minimization. A.E.C. Research and Development Report ANL-599, 1959.

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M. P. Friedlander. A Globally Convergent Linearly Constrained Lagrangian Method for Nonlinear Optimization. 2002.

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P. E. Gill and W. Murray. Numerically stable methods for quadratic programming. Mathematical Programming, 14:349–372, 1978.

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Philip E. Gill, Sven J. Hammarling, Walter Murray, Michael A. Saunders, and Margaret H. Wright. User's guide for LSSOL ((version 1.0): A Fortran package for constrained linear least-squares and convex quadratic programming. Technical Report SOL 86-1, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, California 94305-4022, 1986.

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Philip E. Gill, Walter Murray, and Michael A. Saunders. User's guide for QPOPT 1.0: A Fortran package for Quadratic programming. Technical Report SOL 95-4, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, California 94305-4022, 1995.

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Philip E. Gill, Walter Murray, Michael A. Saunders, and Margaret H. Wright. User's guide for NPSOL 5.0: A Fortran package for nonlinear programming. Technical Report SOL 86-2, Revised July 30, 1998, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, California 94305-4022, 1998.

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Jr. J. E. Dennis and R. B. Schnabel. Numerical Methods for Unconstrained Optimization. 1983.

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Bruce A. Murtagh and Michael A. Saunders. MINOS 5.5 USER'S GUIDE. Technical Report SOL 83-20R, Revised July 1998, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, California 94305-4022, 1998.

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M. A. Saunders P. E. Gill, W. Murray and M. H. Wright. Two step-length algorithms for numerical optimization. 1979.

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M. A. Saunders P. E. Gill, W. Murray and M. H. Wright. Procedures for optimization problems with a mixture of bounds and general linear constraints. ACM Transactions on Mathematical Software, 10:282–298, 1984.

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M. A. Saunders P. E. Gill, W. Murray and M. H. Wright. Maintaining lu factors of a general sparse matrix. Linear Algebra and its Applications, 88, 1987.

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M. A. Saunders P. E. Gill, W. Murray and M. H. Wright. A practical anti-cycling procedure for linearly constrained optimization. Mathematical Programming, 45:437–474, 1989.

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M. A. Saunders P. E. Gill, W. Murray and M. H. Wright. A practical anti-cycling procedure for linearly constrained optimization. Mathematical Programming, 45:437–474, 1989.

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M. A. Saunders P. E. Gill, W. Murray and M. H. Wright. Inertia-controlling methods for general quadratic programming. SIAM Review, 33:1–36, 1991.

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W. Murray P. E. Gill and M. A. Saunders. User's guide for npopt: a fortran package for nonlinear programming.

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W. Murray P. E. Gill and M. H. Wright. Practical Optimization. 1981.

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P. M. Pardalos and G. Schnitger. Checking local optimality in constrained quadratic programming is NP-hard. Operations Research Letters, 7:33–35, 1988.

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J. K. Reid. Fortran subroutines for handling sparse linear programming bases. Report R8269, 1976.

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J. K. Reid. A sparsity-exploiting variant of the bartels-golub decomposition for linear programming bases. Mathematical Programming, 24:55–69, 1982.

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S. M. Robinson. A quadratically convergent algorithm for general nonlinear programming problems. Mathematical Programming, 3:145–156, 1972.

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P. Wolfe. The reduced-gradient method. 1962.

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