Systems Optimization Laboratory
Stanford, CA 943054121 USA

SOL Technical Reports
To request hard copies of SOL reports, for files not downloadable here,
please email Walter Murray:
walter@stanford.edu
A few OR reports are included from the
Department of Operations Research.
2020
2017
 D. Ma, K. L. Judd, D. Orban, and M. A. Saunders (2017),
Stabilized optimization via an NCL algorithm,
working paper, Stanford University, Dec 2017, 13 pages.
Revised as
D. Ma, K. L. Judd, D. Orban and M. A. Saunders,
Stabilized optimization via an NCL algorithm,
pp 173191 in M. AlBaali et al. (eds.),
Numerical Analysis and Optimization, NAOIV, Muscat, Oman,
January 2017, Springer Proceedings in Mathematics and Statistics, Volume 235,
Springer International Publishing AG (2018).
2015
2014
 D. Ma and M. A. Saunders (2014),
Solution of multiscale linear programs using Quad precision,
Report SOL 20141, Apr 2014, 5 pages.
Revised 24 Aug 2014 as
Solving multiscale linear programs using the simplex method
in quadruple precision, pp 223235 in
M. AlBaali, L. Grandinetti, and A. Purnama (eds.),
Numerical Analysis and Optimization, NAOIII, Muscat, Oman,
Springer Proceedings in Mathematics and Statistics, Volume 134,
Springer International Publishing Switzerland (2015).
2013
 J. D. Lee, Y. Sun, and M. A. Saunders (2013),
Proximal Newtontype methods for minimizing composite functions,
Report SOL 20131, revised Mar 2014, 24 pages.
 Y. Sun, R. M. T. Fleming, I. Thiele, and M. A. Saunders (2013),
Robust flux balance analysis of multiscale biochemical reaction networks,
Report SOL 20132, 8 pages.
Published
BMC Bioinformatics 14:240 (2013).
Local copy:
BMCBioinformatics2013robustFBA.pdf.
2011
 R. M. T. Fleming, C. M. Maes, M. A. Saunders,
Y. Ye and B. Ø. Palsson (2011),
A variational principle
for computing nonequilibrium fluxes and potentials
in genomescale biochemical networks,
Report SOL 20111, 17 pages.
Submitted 5 Apr 2011 to J. of Theoretical Biology.
Accepted 26 Sep 2011.
Published
J. of Theoretical Biology 292 (2012) 7177.
Local copy: FleMSYP2012.pdf.
 D. C.L. Fong and M. A. Saunders (2011),
CG versus MINRES: An empirical comparison,
Report SOL 20112R, to appear in
SQU Journal for Science, 17:1 (2012), 4462.
 S. Akle, O. A. Dalal, R. M. T. Fleming, M. A. Saunders, N. A. Taheri, and Y. Ye (2011),
Existence of positive steady states
for mass conserving and massaction chemical reaction networks
with a single terminallinkage class,
Report SOL 20113, 16 pages.
Submitted 25 Oct 2011 to J. of Mathematical Biology.
2010
 V. Pereyra, M. A. Saunders, and J. Castillo (2010),
Equispaced Pareto front construction for
constrained biobjective optimization,
Report SOL 20101, 15 pages.
Published in
Mathematical and Computer Modelling, available online Feb 2011.
 D. C.L. Fong and M. A. Saunders (2010),
LSMR: An iterative algorithm
for sparse leastsquares problems,
Report SOL 20102R1 (revised Mar 14, 2011), 21 pages.
SIAM J. Sci. Comput. 33:5, 29502971,
published electronically Oct 27, 2011.
 D. C.L. Fong and M. A. Saunders (2010),
LSMR: An iterative algorithm
for sparse leastsquares problems,
Report SOL 20102, 22 pages.
This version contains Section 10.4, a suggestion for using the
GolubKahan process to compute singular vectors of dense matrices.
 S.C. T. Choi, C. C. Paige and M. A. Saunders (2010),
MINRESQLP:
A Krylov subspace method for indefinite or singular symmetric systems,
Report SOL 20103, 26 pages.
SIAM J. Sci. Comput., submitted 08 Mar 2010,
revised 30 Mar 2011, accepted Apr 27, 2011.
SIAM J. Sci. Comput. 33:4, 18101836,
published electronically Aug 4, 2011.
2009
2008
2007
2006
2004
2001
 A. De Miguel and W. Murray (2001), Two decomposition algorithms for
nonconvex optimization problems with global variables, Report SOL 20011,
32 pages.
 A. De Miguel and W. Murray (2001), Generating optimization
problems with global variables, Report SOL 20012, 14 pages.
 T. Dorstenstein (2001), Constructive and exchange algorithms for the frequency
assignment problem, Report SOL 20013, 20 pages.
2000
 A. Gupta and W. Murray (2000), Optimal investment with behavioral utilities
using a binomial tree model for assetreturns, Report SOL 20001, 31 pages.
 A. Gupta and W. Murray (2000), How to spend and invest retirement savings,
Report SOL 20002, 25 pages.
1999
 G. Infanger (1999),
Managing risk using multistage stochastic optimization,
Report SOL 992, Dept of EESOR, Stanford University, 57 pages.
 A. George and M. A. Saunders (1999),
Solution of sparse linear equations using Cholesky factors of augmented systems,
Report SOL 991, Dept of EESOR, Stanford University, 9 pages.
Revised Oct 26, 2000 (draft), 12 pages.
1998
1997
 R. Entriken (1997), Language constructs for modeling stochastic linear
programs, Report SOL 971, 17 pages.
 R. Entriken & S. Voessner (1997), Genetic algorithms for production
simulation, Report SOL 972, 14 pages.
 P. E. Gill, W. Murray, and M. A. Saunders (1997),
SNOPT:
An SQP algorithm for largescale constrained optimization, Report SOL
973, Dept of EESOR, Stanford University, 37 pages.
 S. Voessner, M. O’Sullivan, & U. Kausch (1997), Improving
the efficiency of genetic algorithms for constrained optimization, Report
SOL 974, 9 pages.
 S. Voessner (1997), Convergence measures for genetic algorithms, Report
SOL 975, 10 pages.
 I. Bongartz, A. R. Conn, N. I. M. Gould, M. A. Saunders and Ph. L. Toint
(1997), A
numerical comparison between the LANCELOT and MINOS packages for largescale
constrained optimization, Report SOL 976, Dept of EESOR, Stanford University,
19 pages.
 I. Bongartz, A. R. Conn, N. I. M. Gould, M. A. Saunders and Ph. L. Toint
(1997), A numerical
comparison between the LANCELOT and MINOS packages for largescale constrained
optimization: the complete results, Report SOL 977, Dept of EESOR, Stanford
University, 50 pages.
 M. O’Sullivan (1997), Linking MINOS & MATLAB, Report SOL
978, 27 pages.
1996
 M. A. Saunders (1996), Computing projections with LSQR,
Report SOL 961, 8 pages.
In BIT 37:1 (1997) 96104.
 M. Prindiville (1996), Advances in the application of stochastic programming
techniques in mortgage finance, Report SOL 962, 85 pages.
 M. A. Saunders and J. A. Tomlin (1996),
Stable reduction to KKT systems
in barrier methods for linear and quadratic programming,
Report SOL 963, Dept of EESOR, Stanford University, 9 pages.
 M. A. Saunders and J. A. Tomlin (1996),
Solving regularized linear programs
using barrier methods and KKT systems,
Report SOL 964, Dept of EESOR, Stanford University, 12 pages.
1995
 M. A. Saunders (1995), Choleskybased
methods for sparse least squares: The benefits of regularization, Report
SOL 951, Dept of Operations Research, Stanford University, 10 pages. In L. Adams and
J. L. Nazareth (eds.), Linear and nonlinear conjugate gradientrelated methods,
SIAM, Philadelphia, 92100.
 G. Infanger (1995), Scheduling using relaxation and decomposition, Report
SOL 952, 20 pages.
 W. Murray and F. Prieto (1995), A secondderivative method for nonlinearly
constrained optimization, Report SOL 953, 48 pages.
 P. E. Gill, W. Murray, and M. A. Saunders (1995),
User's
guide for QPOPT 1.0: A Fortran package for quadratic programming, Report
SOL 954, Dept of Operations Research, Stanford University, 38 pages.
 R. Entriken and C. Yu, (1995), Absolute deviation as a measure of risk,
Report SOL 955, 9 pages.
 G. B. Dantzig and G. Infanger (1995), A Probabilistic lower bound for twostage
stochastic programs, Report SOL 956, 22 pages.
1994
 G. B. Dantzig and G. Infanger (1994), Intelligent control  optimization under
uncertainty for the control of hydro power systems, Report SOL 941, 16 pages.
 G. B. Dantzig and D. Morton (1994), Interstage dependency in multistage stochastic
linear programming, Report SOL 942, 17 pages.
 A. Forsgren and W. Murray (1994), Newton methods for largescale linear
inequalityconstrained minimization, Report SOL 943, 17 pages.
 M. A. Saunders (1994), Solution of sparse rectangular systems using
LSQR and CRAIG, Report SOL 944, 14 pages.
In BIT 35 (1996) 588604.
1993
 A. Forsgren, P. E. Gill and W. Murray (1993), Computing modified Newton
directions using a partial Cholesky factorization, Report
SOL 931, 14 pages.
 S. Guu and R. W. Cottle (1993), On processing a class of
linear complementarity problems by a perturbation method, Report SOL 932,
17 pages.
 W. Murray and F. Prieto (1993), A sequential quadratic
programming algorithm using an incomplete solution of the subproblem, Report
SOL 933, 53 pages.
 P. E. Gill, M. A. Saunders and J. Shinnerl (1993), On
the numerical stability of quasidefinite systems, Report SOL 934, 8 pages.
See On the stability of Cholesky factorization for quasidefinite systems,
SIAM Journal on Matrix Analysis and Applications. 17(1), 3546 (1996).
 H. Chen, P. Pardalos and M. A. Saunders (1993),
The simplex algorithm with a new primal and dual pivot rule, Report
SOL 935, 8 pages.
 D. Morton (1993), Algorithmic advances in stochastic programming, Report
SOL 936, (1993), 115 pages.
 G. Infanger (1993), Decomposition and (importance) sampling techniques
for multistage stochastic linear programs, Report SOL 937, 41 pages.
 A. Krishna (1993), Enhanced algorithms for stochastic programming, Report
SOL 938, 83 pages.
1992
 S. A. Leichner, G. B. Dantzig and J. W. Davis (1992), A strictly improving
phase I algorithm using leastsquares subproblems, Report SOL 921.
See A strictly improving linear programming Phase I algorithm,
Annals of Operations Research 46/47 (1993), 409430.
 S. A. Leichner, G. B. Dantzig and J. W. Davis (1992), A strictly improving
linear programming algorithm based on a series of phase I problems,
Report SOL 922.
See A strictly improving linear programming Phase I algorithm,
Annals of Operations Research 46/47 (1993), 409430.
 L. Mathiesen (1992), Pricing of electricity in the presence of water uncertainty,
Report SOL 923.
 S. Eldersveld (1992), Largescale sequential quadratic programming algorithms,
Report SOL 924.
 G. B. Dantzig (1992), An epsilonprecise
feasible solution to a linear program with a convexity constraint
in 1/eps^2 iterations independent of problem size,
Report SOL 925.
Submitted to Mathematical Programming Series B.
 G. B. Dantzig (1992), Bracketing to speed convergence
illustrated on the von Neumann algorithm for finding a feasible solution
to a linear program with a convexity constraint,
Report SOL 926.
 S. Guu and R. W. Cottle (1992), Notes on Po and its subclasses, Report
SOL 927.
 G. Infanger (1992), Planning under uncertaintysolving largescale stochastic
linear programs, Report SOL 928. Published as a book.
1991
 F. Jarre, F. and M. A. Saunders (1991), An adaptive primaldual method
for linear programming, Report SOL 911.
 D. B. Ponceleon (1991), Barrier methods for largescale quadratic programming,
Report SOL 912.
 P. E. Gill, W. Murray, D. B. Ponceleon and M. A. Saunders (1991), Primaldual
methods for linear programming, Report SOL 913.
 G. B. Dantzig, and G. Infanger (1991), Largescale stochastic linear programs:
importance sampling and Benders decomposition,
Report SOL 914.
Submitted for Publication in Mathematical Programming.
 G. B. Dantzig (1991), Converting a converging algorithm into a polynomially
bounded algorithm,
Report SOL 915.
 G. Infanger (1991), Monte Carlo (importance) sampling within a Benders
decomposition algorithm for stochastic linear programs, Report SOL 916.
In Annals of Operations Research 39 (1992) 6995.
 P. E. Gill, W. Murray, D. B. Ponceleon and M. A. Saunders (1991), Solving
reduced KKT systems in barrier methods for linear and quadratic programming,
Report SOL 917.
 F. Jarre (1991), An interiorpoint method for minimizing the maximum eigenvalue
of a linear combination of matrices, Report SOL 918.
 F. Jarre and M. A. Saunders (1991), Practical aspects of an interiorpoint
method for convex programming, Report SOL 919.
 G. B. Dantzig, J. K. Ho and G. Infanger (1991), Solving stochastic linear
programs on a hypercube multicomputer, Report SOL 9110.
Submitted for Publication in Operations Research.
 G. B. Dantzig and G. Infanger (1991), Multistage stochastic linear programs
for portfolio optimization, Report SOL 9111.
In Proceedings of the Annual Symposium of RAMP (Research
Association of Mathematical Programming) Tokyo, November 1991.
1990
 S. K. Eldersveld and M. C. Rinar (1990), A vectorization
algorithm for the solution of large, sparse triangular systems of equations,
Report SOL 901.
 S. K. Eldersveld and M. A. Saunders (1990), A blockLU
update for largescale linear programming, Report SOL 902.
In SIAM Journal on Matrix Analysis and Applications 13 (1992), 191201.
 P. H. McAllister, J. C. Stone and G. B. Dantzig (1990),
An interactive model management system: user interface and system design,
Report SOL 903
 G. B. Dantzig and Yinyu Ye (1990), A buildup interior
method for linear programming. Report SOL 904.
Submitted to Mathematical Programming.
 J. Yao (1990), A generalized complementarity problem
in hilbert space, Report SOL 905. Submitted
to Journal of Mathematical Analysis and Applications.
 A. L. Forsgren and W. Murray (1990), Newton
methods for largescale linear equalityconstrained minimization, Report
SOL 906.
 J. Yao (1990), Monotone complementarity problem in
hilbert space, Report SOL 907. Submitted to
Bulletin of the Australian Mathematical Society.
 P. E. Gill, W. Murray, D. B. Ponceleon and M. A.
Saunders (1990), Preconditioners for indefinite systems arising in optimization,
Report SOL 908.
In SIAM Journal on Matrix Analysis and Applications. 13 (1992), 292311.
 R. W. Cottle and YowYieh Chang (1990), LeastIndex
Resolution of degeneracy in linear complementarity problems with sufficient
matrices, Report SOL 909. Submitted for
Publication in SIAM Journal on Matrix Analysis and Applications.
 R. W. Cottle and JenChih Yao (1990), Pseudomonotone
complementarity problems in hilbert space, Report SOL
9010. In Journal of Optimization Theory and Applications,
75(2), November 1992.
 E. Schweitzer (1990), Modifying MINOS for solving
the dual of a linear program, Report SOL 9011.
Submitted to Mathematical Programming.
 W. Murray and F. J. Prieto (1990), A sequential quadratic
programming algorithm using an incomplete solution of the subproblem, Report
SOL 9012.
 W. Murray and F. J. Prieto (1990), A secondderivative
method for nonlinearly constrained optimization,
Report SOL 9013.
 B. C. Eaves and A. J. Hoffman (1990), Covers by polars
of arrangements, Report SOL 9014.
 B. C. Eaves and U. G. Rothblum (1990), A discountedcost
continuoustime flexible manufacturing and operator scheduling model solved
by deconvexification over time, Report SOL
9015.
 F. Jarre (1990), Interiorpoint methods for convex
programming, Report SOL 9016. Accepted for publication
in Applied Mathematics and Optimization.
 R. W. Cottle and SyMing Guu (1990), Two characterizations
of sufficient matrices, Report SOL 9017.
1989
 H. Hu (1989), On the feasibility of a generalized
linear program, Report SOL 891.
 H. Hu (1989), Semiinfinite programming, Report SOL
892. Accepted for publication in Mathematical Programming.
 R. W. Cottle (1989), The principal pivoting method
revisited, Report SOL 893. Published in Mathematical Programming 48, Series
B, (1990) NorthHolland, Pp. 369385.
 A. Krishna (1989), Note On Degeneracy, Report SOL
894. Submitted for Publication in Mathematical Programming.
 K. Zikan (1989), An efficient exact algorithm for
the "LEASTSQUARES" image registration problem, Report SOL 895. Accepted
for publication in Pattern Analysis and Machine Intelligence.
 A. Marxen (1989 Ph.D. thesis), Primal barrier
methods for linear programming, Report SOL 896.
 F. Prieto (1989 Ph.D. thesis), Sequential quadratic
programming algorithms for optimization, Report SOL 897.
 A. Diener (1989 Ph.D. thesis), Nearoptimal
operation of a multiplant manufacturing system with central procurement,
Report SOL 898.
 A. Diener (1989 Ph.D. thesis), Nearoptimal
operation of a single machine with continuous buffer feed, Report SOL 899.
 P. F. De Mazancourt (1989 Ph.D. thesis), A
matrix factorization and its application to largescale linear programming,
Report SOL 8910.
 A. L. Forsgren, P. E. Gill and W. Murray (1989),
On the identification of local minimizers in inertiacontrolling methods
for quadratic programming, Report SOL 8911.
 A. L. Forsgren, P. E. Gill and W. Murray (1989),
A modified Newton method for unconstrained minimization, Report SOL 8912.
 G. Infanger (1989), Monte Carlo (importance) sampling
within a Benders decomposition algorithm for stochastic linear programs,
Report SOL 8913.
 B. C. Eaves and U. G. Rothblum (1989) A class of
"ONTO" multifunctions, Report SOL 8914.
 J. Yao (1989), Generalized quasivariational inequality and implicit complementarity problems, Report SOL 8915.
"The generalized implicit complementarity problem with applications" to appear in Journal
of Mathematical Analysis and Applications. "The generalized implicit complementarity
problem" submitted to Journal of Mathematical Analysis and Applications.
 J. Yao (1989), A basic theorem of complementarity
for the generalized variational like inequality problem, Report SOL 8916.
To appear in Journal of Mathematical Analysis and Applications.
 R. Entriken (1989 Ph.D. thesis), The parallel
decomposition of linear programs, Report SOL 8917. Chapter 4 submitted to
ORSA Journal on Computing.
 J. Yao (1989), On mean value iterations with application
to variational inequality problems, Report SOL 8918.
 J. Yao (1989), Fixed points by Ishikawa Iterations,
Report SOL 8919. Submitted to Journal of Mathematical Analysis and
Applications.
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