M. Argaez, R. A. Tapia, and L. Velazquez, Numerical Comparisons of Path-Following Strategies for a Primal-Dual Interior-Point Method for Nonlinear Programming, Journal of Optimization Theory and Applications, Vol. 114, No. 2, 2002.
B. M. Averick, R. G. Carter, J. J. More, and G.-L. Xue, The MINPACK-2 test problem collection, Preprint MCS-P153-0692, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois, 1992.
A. R. Conn, N. I. M. Gould, and Ph. L. Toint, Convergence of quasi-Newton matrices generated by the symmetric rank one update, Mathematical Programming, Vol. 50 pp. 177--195, 1991.
R. B. Davies, NEWMAT11: a matrix manipulation library. See http://www.robertnz.net.
J. E. Dennis, Jr. and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall Inc., New Jersey, 1983.
J. E. Dennis, Jr. and V. Torczon, Direct Search Methods on Parallel Machines, SIAM J. Optimization, Vol. 1, No. 4, pp. 448--474, November 1991.
J. J. Dongarra, J. Du Croz, I. S. Duff, and S. Hammarling, A set of Level 3 Basic Linear Algebra Subprograms, ACM Trans. Math. Software, Vol. 16, pp. 18--28, 1990.
J. J. Dongarra, J. Du Croz, S. Hammarling, and R. J. Hanson, An extended set of FORTRAN Basic Linear Algebra Subprograms, ACM Trans. Math. Software, Vol. 14, pp. 1--17, 1988.
A. S. El-Bakry, R. A. Tapia, T. Tsuchiya and Y. Zhang, On the Formulation and Theory of the Newton Interior-Point Method for Nonlinear Programming, Journal of Optimization Theory and Applications, Vol. 89, pp. 507--541, 1996.
A. S. El-Bakry, R. A. Tapia, and Y. Zhang, A Study of Indicators for Identifying Zero Variables in Interior-Point Methods, SIAM Review, Vol. 36, No. 1, pp. 45--72, 1994.
F. Facchinei, A. Fischer, and C. Kanzow, On the Accurate Identification of Active Constraints, SIAM J. Optimization, Vol. 9, No. 1, pp. 14--32, 1998.
P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright, User's Guide for NPSOL(Version 4.0): A Fortran Package for Nonlinear Programming, Technical Report SOL-86-2, System Optimization Laboratory, Stanford University, Stanford, CA, 1986.
P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization , Academic Press, London, 1981.
M. J. Goldsmith, Sequential Quadratic Programming Methods Based on Indefinite Hessian Approximations, Ph.D. Thesis, Department of Operations Research, Stanford University, Palo Alto, CA, March 1999.
W. Hock and K. Schittkowski, Test examples for nonlinear programming code, Springer Verlag, New York, 1981.
P. D. Hough and J. C. Meza, A Class of Trust-Region Methods for Parallel Optimization, SIAM J. Optimization, Vol. 13, No. 1, pp. 264--282, 2002.
V. E. Howle, S. M. Shontz, and P. D. Hough, Some Parallel Extensions to Optimization Methods in OPT++ , Sandia Technical Report SAND2000-8877, Sandia National Laboratories, Livermore, CA, October 2000.
C. L. Lawson, R. J. Hanson, D. Kincaid, and F. T. Krogh, Basic Linear Algebra Subprograms for FORTRAN usage, ACM Trans. Math. Software, Vol. 5 pp. 308--329, 1979.
D. Liu and J. Nocedal, On the limited memory BFGS method for large scale optimization, Mathematical Programming B, Vol. 45, pp. 503-528, 1989.
J. C. Meza, OPT++: An Object-Oriented Class Library for Nonlinear Optimization, Sandia Technical Report SAND94-8225, Sandia National Laboratories, Livermore, CA, March 1994.
J. More and D. Thuente, Line Search Algorithms with Guaranteed Sufficient Decrease, ACM Transactions on Mathematical Software, Vol. 20, No. 3, pp. 286--307, 1994.
W. Murray and M. H. Wright, Line search procedures for the logarithmic barrier function, SIAM J. Optimization, Vol. 4, No. 2, pp. 229--246, 1994.
P. S. Pacheco, Parallel Programming with MPI, Morgan Kaufmann Publishers, Inc., San Francisco, 1997.
R. A. Tapia, On the role of slack variables in quasi-Newton methods for constrained optimization, Numerical Optimization of Dynamic Systems, In L. C. W. Dixon and G.P. Szego, eds., North Holland, pp. 235--246, 1980.
R. J. Vanderbei and D. Shanno, An interior-point algorithm for nonconvex nonlinear programming, Computational Optimization and Applications, Vol. 13, pp. 231--259, 1999.
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