Michael Saunders

Professor (Research),
Management Science and Engineering
Institute for Computational and Mathematical Engineering, Stanford University

Office: Terman 330
Phone: 650.723.1875
Fax: 650.723.1614
Email: saunders @ stanford.edu

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Publications

1. C. C. Paige and M. A. Saunders, Solution of sparse indefinite systems of linear equations, SINUM 12, 617-629 (1975).
2. B. A. Murtagh and M. A. Saunders, Large-scale linearly constrained optimization, Math. Prog. 14, 41-72 (1978).
3. B. A. Murtagh and M. A. Saunders, A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints, Math. Prog. Study 16 (Constrained Optimization), 84-117 (1982).
4. C. C. Paige and M. A. Saunders, LSQR: An algorithm for sparse linear equations and sparse least squares, ACM TOMS 8(1), 43-71 (1982).
5. C. C. Paige and M. A. Saunders, Algorithm 583; LSQR: Sparse linear equations and least-squares problems, ACM TOMS 8(2), 195-209 (1982).
6. P. E. Gill, W. Murray, M. A. Saunders and M. H. Wright, Sparse matrix methods in optimization, SISSC 5, 562-589 (1984).
7. P. E. Gill, W. Murray, M. A. Saunders, J. A. Tomlin and M. H. Wright, On projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method, Math. Prog. 36, 183-209 (1986).
8. P. E. Gill, W. Murray, M. A. Saunders and M. H. Wright, Maintaining LU factors of a general sparse matrix, LAA 88/89, 239-270 (1987).
9. S. K. Eldersveld and M. A. Saunders, A block-LU update for large-scale linear programming, SIMAX 13, 191-201 (1992).
10. P. E. Gill, W. Murray, D. B. Ponceleón and M. A. Saunders, Preconditioners for indefinite systems arising in optimization, SIMAX 13, 292-311 (1992).
11. M. A. Saunders, Major Cholesky would feel proud, ORSA J. on Computing 6, 23-27 (1994).
12. B. A. Murtagh and M. A. Saunders, MINOS 5.5 User's Guide, Report SOL 83-20R, Dept of Operations Research, Stanford University (Revised Jul 1998).
13. M. A. Saunders, Solution of sparse rectangular systems using LSQR and CRAIG, BIT 35, 588-604 (1995).
14. P. E. Gill, M. A. Saunders and J. R. Shinnerl, On the stability of Cholesky factorization for quasi-definite systems, SIMAX 17(1), 35-46 (1996).
15. M. A. Saunders, Cholesky-based methods for sparse least squares: The benefits of regularization, Report SOL 95-1, Dept of Operations Research, Stanford University (1995). In L. Adams and J. L. Nazareth (eds.), Linear and Nonlinear Conjugate Gradient-Related Methods, SIAM, Philadelphia, 92-100 (1996).
16. P. E. Gill, W. Murray and M. A. Saunders, User's guide for QPOPT 1.0: A Fortran package for quadratic programming, Report SOL 95-4, Dept of Operations Research, Stanford University (1995).
17. M. A. Saunders and J. A. Tomlin, Stable reduction to KKT systems in barrier methods for linear and quadratic programming, Report SOL 96-3, Dept of EESOR, Stanford University (1996).
18. M. A. Saunders and J. A. Tomlin, Solving regularized linear programs using barrier methods and KKT systems, Report SOL 96-4, Dept of EESOR, Stanford University (1996).
19. M. A. Saunders, Computing projections with LSQR, BIT 37:1, 96-104 (1997).
20. S. S. Chen, D. L. Donoho and M. A. Saunders, Atomic decomposition by Basis Pursuit, SISC 20(1), 33-61 (1998).
21. P. E. Gill, W. Murray and M. A. Saunders, SNOPT: An SQP algorithm for large-scale constrained optimization, Report SOL 97-3, Dept of EESOR, Stanford University (1997), 37 pages.
22. I. Bongartz, A. R. Conn, N. I. M. Gould, M. A. Saunders and Ph. L. Toint, A numerical comparison between the LANCELOT and MINOS packages for large-scale constrained optimization, Report SOL 97-6, Dept of EESOR, Stanford University (1997), 19 pages.
23. I. Bongartz, A. R. Conn, N. I. M. Gould, M. A. Saunders and Ph. L. Toint, A numerical comparison between the LANCELOT and MINOS packages for large-scale constrained optimization: the complete results, Report SOL 97-7, Dept of EESOR, Stanford University (1997), 50 pages.
24. P. E. Gill, W. Murray and M. A. Saunders, User's guide for SNOPT 5.3: A Fortran package for large-scale nonlinear programming, Report SOL 98-1, Dept of EESOR, Stanford University (1997), 37 pages.
25. M. A. Saunders, Solution of sparse linear equations using Cholesky factors of augmented systems, Report SOL 99-1, Dept of EESOR, Stanford University (1999), 9 pages.

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Research Interests

Fields of Specialization

• Numerical optimization, numerical linear algebra.

Interests

• Linear programming, nonlinear programming, sparse matrix methods, iterative solvers.
  Design and implementation of algorithms for constrained optimization and sparse linear equations (including sparse least squares).

Co-author of constrained optimization packages

• MINOS, NPSOL, LSSOL, QPOPT, SQOPT, SNOPT.
  • See Stanford Business Software, Inc. for descriptions of each package.
  • Stanford users and UCSD users may obtain code and manuals free.
  • Please come and chat about your application:
    saunders @ Stanford.edu or walter @ Stanford.edu and pgill @ ucsd.edu (respectively).
  • Matlab interface to MINOS:  CMEX files.

  Co-author of iterative linear equation solvers:

  • SYMMLQ (symmetric indefinite systems)
    Fortran 77 files | Matlab files
  • LSQR (unsymmetric systems and least squares)
    Fortran 77 files | Matlab files

  I'm always glad to see output from MINOS, SYMMLQ, LSQR, etc.

  If you're having trouble I'll try to help.
  Send me email: saunders @ Stanford.edu
  (Attachments are OK, but please, no MS WORD documents!)

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