Systems Optimization Laboratory

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.

2014

• D. Ma and M. A. Saunders (2014), Solution of multiscale linear programs using Quad precision, Report SOL 2014-1, Apr 2014, 5 pages.
  Revised 24 Aug 2014 as Solving multiscale linear programs using the simplex method in quadruple precision, to appear in M. Al-Baali, L. Grandinetti, and A. Purnama (eds.), Recent Developments in Numerical Analysis and Optimization, Springer Proceedings in Mathematics and Statistics.

2013

• J. D. Lee, Y. Sun, and M. A. Saunders (2013), Proximal Newton-type methods for minimizing composite functions, Report SOL 2013-1, 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 2013-2, 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 genome-scale biochemical networks, Report SOL 2011-1, 17 pages. Submitted 5 Apr 2011 to J. of Theoretical Biology. Accepted 26 Sep 2011. Published J. of Theoretical Biology 292 (2012) 71-77. Local copy: FleMSYP2012.pdf.

• D. C.-L. Fong and M. A. Saunders (2011), CG versus MINRES: An empirical comparison, Report SOL 2011-2R, to appear in SQU Journal for Science, 17:1 (2012), 44--62.
• 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 mass-action chemical reaction networks with a single terminal-linkage class, Report SOL 2011-3, 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 2010-1, 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 least-squares problems, Report SOL 2010-2R1 (revised Mar 14, 2011), 21 pages. SIAM J. Sci. Comput. 33:5, 2950-2971, published electronically Oct 27, 2011.

• D. C.-L. Fong and M. A. Saunders (2010), LSMR: An iterative algorithm for sparse least-squares problems, Report SOL 2010-2, 22 pages. This version contains Section 10.4, a suggestion for using the Golub-Kahan process to compute singular vectors of dense matrices.

• S.-C. T. Choi, C. C. Paige and M. A. Saunders (2010), MINRES-QLP: A Krylov subspace method for indefinite or singular symmetric systems, Report SOL 2010-3, 26 pages. SIAM J. Sci. Comput., submitted 08 Mar 2010, revised 30 Mar 2011, accepted Apr 27, 2011. SIAM J. Sci. Comput. 33:4, 1810-1836, published electronically Aug 4, 2011.

2009

• E. Kostina, M. A. Saunders, and I. Schierle, Computation of covariance matrices for constrained parameter estimation problems using LSQR, Report SOL 2009-1, 11 pages.

2008

• P. W. Glynn and G. Infanger (2008), Simulation-based confidence bounds for two-stage stochastic programs, Report SOL 2008-1, 18 pages.

2007

• J. F. Grcar, M. A. Saunders, and Z. Su (2007), Estimates of optimal backward perturbations for linear least squares problems, Report SOL 2007-1, 21 pages.

2006

• M. J. O'Sullivan and M. A. Saunders (2006), Stabilizing policy improvement for large-scale infinite-horizon dynamic programming, Report SOL 2006-1, 19 pages. Published in SIAM J. Matrix. Anal. Appl. 31:2 (2009), 434-459.

2004

• T.-C. Liang, T.-C. Wang, and Y. Ye (2004), A gradient search method to round the semidefinite programming relaxation solution for ad hoc wireless sensor network localization, Report SOL 2004-2, 27 pages.

2001

• A. De Miguel and W. Murray (2001), Two decomposition algorithms for nonconvex optimization problems with global variables, Report SOL 2001-1, 32 pages.
• A. De Miguel and W. Murray (2001), Generating optimization problems with global variables, Report SOL 2001-2, 14 pages.
• T. Dorstenstein (2001), Constructive and exchange algorithms for the frequency assignment problem, Report SOL 2001-3, 20 pages.

• A. Gupta and W. Murray (2000), Optimal investment with behavioral utilities using a binomial tree model for asset-returns, Report SOL 2000-1, 31 pages.
• A. Gupta and W. Murray (2000), How to spend and invest retirement savings, Report SOL 2000-2, 25 pages.

• G. Infanger (1999), Managing risk using multi-stage stochastic optimization, Report SOL 99-2, 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 99-1, Dept of EESOR, Stanford University, 9 pages. Revised Oct 26, 2000 (draft), 12 pages.

• P. E. Gill, W. Murray, and M. A. Saunders (1998), User's guide for SNOPT 5.3: A Fortran package for large-scale nonlinear programming, Report SOL 98-1, 67 pages.

• R. Entriken (1997), Language constructs for modeling stochastic linear programs, Report SOL 97-1, 17 pages.
• R. Entriken & S. Voessner (1997), Genetic algorithms for production simulation, Report SOL 97-2, 14 pages.
• P. E. Gill, W. Murray, and M. A. Saunders (1997), SNOPT: An SQP algorithm for large-scale constrained optimization, Report SOL 97-3, 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 97-4, 9 pages.
• S. Voessner (1997), Convergence measures for genetic algorithms, Report SOL 97-5, 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 large-scale constrained optimization, Report SOL 97-6, 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 large-scale constrained optimization: the complete results, Report SOL 97-7, Dept of EESOR, Stanford University, 50 pages.
• M. O’Sullivan (1997), Linking MINOS & MATLAB, Report SOL 97-8, 27 pages.

• M. A. Saunders (1996), Computing projections with LSQR, Report SOL 96-1, 8 pages. In BIT 37:1 (1997) 96-104.
• M. Prindiville (1996), Advances in the application of stochastic programming techniques in mortgage finance, Report SOL 96-2, 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 96-3, 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 96-4, Dept of EESOR, Stanford University, 12 pages.

• M. A. Saunders (1995), Cholesky-based methods for sparse least squares: The benefits of regularization, Report SOL 95-1, Dept of Operations Research, Stanford University, 10 pages. In L. Adams and J. L. Nazareth (eds.), Linear and nonlinear conjugate gradient-related methods, SIAM, Philadelphia, 92-100.
• G. Infanger (1995), Scheduling using relaxation and decomposition, Report SOL 95-2, 20 pages.
• W. Murray and F. Prieto (1995), A second-derivative method for nonlinearly constrained optimization, Report SOL 95-3, 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 95-4, Dept of Operations Research, Stanford University, 38 pages.
• R. Entriken and C. Yu, (1995), Absolute deviation as a measure of risk, Report SOL 95-5, 9 pages.
• G. B. Dantzig and G. Infanger (1995), A Probabilistic lower bound for two-stage stochastic programs, Report SOL 95-6, 22 pages.

• G. B. Dantzig and G. Infanger (1994), Intelligent control - optimization under uncertainty for the control of hydro power systems, Report SOL 94-1, 16 pages.
• G. B. Dantzig and D. Morton (1994), Interstage dependency in multistage stochastic linear programming, Report SOL 94-2, 17 pages.
• A. Forsgren and W. Murray (1994), Newton methods for large-scale linear inequality-constrained minimization, Report SOL 94-3, 17 pages.
• M. A. Saunders (1994), Solution of sparse rectangular systems using LSQR and CRAIG, Report SOL 94-4, 14 pages. In BIT 35 (1996) 588-604.

• A. Forsgren, P. E. Gill and W. Murray (1993), Computing modified Newton directions using a partial Cholesky factorization, Report SOL 93-1, 14 pages.
• S. Guu and R. W. Cottle (1993), On processing a class of linear complementarity problems by a perturbation method, Report SOL 93-2, 17 pages.
• W. Murray and F. Prieto (1993), A sequential quadratic programming algorithm using an incomplete solution of the subproblem, Report SOL 93-3, 53 pages.
• P. E. Gill, M. A. Saunders and J. Shinnerl (1993), On the numerical stability of quasi-definite systems, Report SOL 93-4, 8 pages. See On the stability of Cholesky factorization for quasi-definite systems, SIAM Journal on Matrix Analysis and Applications. 17(1), 35--46 (1996).

• H. Chen, P. Pardalos and M. A. Saunders (1993), The simplex algorithm with a new primal and dual pivot rule, Report SOL 93-5, 8 pages.
• D. Morton (1993), Algorithmic advances in stochastic programming, Report SOL 93-6, (1993), 115 pages.
• G. Infanger (1993), Decomposition and (importance) sampling techniques for multi-stage stochastic linear programs, Report SOL 93-7, 41 pages.
• A. Krishna (1993), Enhanced algorithms for stochastic programming, Report SOL 93-8, 83 pages.

• S. A. Leichner, G. B. Dantzig and J. W. Davis (1992), A strictly improving phase I algorithm using least-squares subproblems, Report SOL 92-1. See A strictly improving linear programming Phase I algorithm, Annals of Operations Research 46/47 (1993), 409-430.

• 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 92-2. See A strictly improving linear programming Phase I algorithm, Annals of Operations Research 46/47 (1993), 409-430.

• L. Mathiesen (1992), Pricing of electricity in the presence of water uncertainty, Report SOL 92-3.

• S. Eldersveld (1992), Large-scale sequential quadratic programming algorithms, Report SOL 92-4.
• G. B. Dantzig (1992), An epsilon-precise feasible solution to a linear program with a convexity constraint in 1/eps^2 iterations independent of problem size, Report SOL 92-5. 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 92-6.
• S. Guu and R. W. Cottle (1992), Notes on Po and its subclasses, Report SOL 92-7.
• G. Infanger (1992), Planning under uncertainty--solving large-scale stochastic linear programs, Report SOL 92-8. Published as a book.

• F. Jarre, F. and M. A. Saunders (1991), An adaptive primal-dual method for linear programming, Report SOL 91-1.
• D. B. Ponceleon (1991), Barrier methods for large-scale quadratic programming, Report SOL 91-2.
• P. E. Gill, W. Murray, D. B. Ponceleon and M. A. Saunders (1991), Primal-dual methods for linear programming, Report SOL 91-3.
• G. B. Dantzig, and G. Infanger (1991), Large-scale stochastic linear programs: importance sampling and Benders decomposition, Report SOL 91-4. Submitted for Publication in Mathematical Programming.
• G. B. Dantzig (1991), Converting a converging algorithm into a polynomially bounded algorithm, Report SOL 91-5.
• G. Infanger (1991), Monte Carlo (importance) sampling within a Benders decomposition algorithm for stochastic linear programs, Report SOL 91-6. In Annals of Operations Research 39 (1992) 69-95.
• 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 91-7.
• F. Jarre (1991), An interior-point method for minimizing the maximum eigenvalue of a linear combination of matrices, Report SOL 91-8.
• F. Jarre and M. A. Saunders (1991), Practical aspects of an interior-point method for convex programming, Report SOL 91-9.
• G. B. Dantzig, J. K. Ho and G. Infanger (1991), Solving stochastic linear programs on a hypercube multicomputer, Report SOL 91-10. Submitted for Publication in Operations Research.
• G. B. Dantzig and G. Infanger (1991), Multi-stage stochastic linear programs for portfolio optimization, Report SOL 91-11. In Proceedings of the Annual Symposium of RAMP (Research Association of Mathematical Programming) Tokyo, November 1991.

• S. K. Eldersveld and M. C. Rinar (1990), A vectorization algorithm for the solution of large, sparse triangular systems of equations, Report SOL 90-1.
• S. K. Eldersveld and M. A. Saunders (1990), A block-LU update for large-scale linear programming, Report SOL 90-2. In SIAM Journal on Matrix Analysis and Applications 13 (1992), 191-201.
• P. H. McAllister, J. C. Stone and G. B. Dantzig (1990), An interactive model management system: user interface and system design, Report SOL 90-3
• G. B. Dantzig and Yinyu Ye (1990), A build-up interior method for linear programming. Report SOL 90-4. Submitted to Mathematical Programming.
• J. Yao (1990), A generalized complementarity problem in hilbert space, Report SOL 90-5. Submitted to Journal of Mathematical Analysis and Applications.
• A. L. Forsgren and W. Murray (1990), Newton methods for large-scale linear equality-constrained minimization, Report SOL 90-6.
• J. Yao (1990), Monotone complementarity problem in hilbert space, Report SOL 90-7. 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 90-8. In SIAM Journal on Matrix Analysis and Applications. 13 (1992), 292--311.
• R. W. Cottle and Yow-Yieh Chang (1990), Least-Index Resolution of degeneracy in linear complementarity problems with sufficient matrices, Report SOL 90-9. Submitted for Publication in SIAM Journal on Matrix Analysis and Applications.
• R. W. Cottle and Jen-Chih Yao (1990), Pseudo-monotone complementarity problems in hilbert space, Report SOL 90-10. 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 90-11. 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 90-12.
• W. Murray and F. J. Prieto (1990), A second-derivative method for nonlinearly constrained optimization, Report SOL 90-13.
• B. C. Eaves and A. J. Hoffman (1990), Covers by polars of arrangements, Report SOL 90-14.
• B. C. Eaves and U. G. Rothblum (1990), A discounted-cost continuous-time flexible manufacturing and operator scheduling model solved by deconvexification over time, Report SOL 90-15.
• F. Jarre (1990), Interior-point methods for convex programming, Report SOL 90-16. Accepted for publication in Applied Mathematics and Optimization.
• R. W. Cottle and Sy-Ming Guu (1990), Two characterizations of sufficient matrices, Report SOL 90-17.

• H. Hu (1989), On the feasibility of a generalized linear program, Report SOL 89-1.
• H. Hu (1989), Semi-infinite programming, Report SOL 89-2. Accepted for publication in Mathematical Programming.
• R. W. Cottle (1989), The principal pivoting method revisited, Report SOL 89-3. Published in Mathematical Programming 48, Series B, (1990) North-Holland, Pp. 369-385.
• A. Krishna (1989), Note On Degeneracy, Report SOL 89-4. Submitted for Publication in Mathematical Programming.
• K. Zikan (1989), An efficient exact algorithm for the "LEAST-SQUARES" image registration problem, Report SOL 89-5. Accepted for publication in Pattern Analysis and Machine Intelligence.
• A. Marxen (1989 Ph.D. thesis), Primal barrier methods for linear programming, Report SOL 89-6.
• F. Prieto (1989 Ph.D. thesis), Sequential quadratic programming algorithms for optimization, Report SOL 89-7.
• A. Diener (1989 Ph.D. thesis), Near-optimal operation of a multi-plant manufacturing system with central procurement, Report SOL 89-8.
• A. Diener (1989 Ph.D. thesis), Near-optimal operation of a single machine with continuous buffer feed, Report SOL 89-9.
• P. F. De Mazancourt (1989 Ph.D. thesis), A matrix factorization and its application to large-scale linear programming, Report SOL 89-10.
• A. L. Forsgren, P. E. Gill and W. Murray (1989), On the identification of local minimizers in inertia-controlling methods for quadratic programming, Report SOL 89-11.
• A. L. Forsgren, P. E. Gill and W. Murray (1989), A modified Newton method for unconstrained minimization, Report SOL 89-12.
• G. Infanger (1989), Monte Carlo (importance) sampling within a Benders decomposition algorithm for stochastic linear programs, Report SOL 89-13.
• B. C. Eaves and U. G. Rothblum (1989) A class of "ONTO" multifunctions, Report SOL 89-14.
• J. Yao (1989), Generalized quasi-variational inequality and implicit complementarity problems, Report SOL 89-15. "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 89-16. To appear in Journal of Mathematical Analysis and Applications.
• R. Entriken (1989 Ph.D. thesis), The parallel decomposition of linear programs, Report SOL 89-17. Chapter 4 submitted to ORSA Journal on Computing.
• J. Yao (1989), On mean value iterations with application to variational inequality problems, Report SOL 89-18.
• J. Yao (1989), Fixed points by Ishikawa Iterations, Report SOL 89-19. Submitted to Journal of Mathematical Analysis and Applications.

1987

• I. J. Lustig (1987), An analysis of an available set of linear programming test problems, Report SOL 87-11, 53 pages.

1986

• P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright (1986), User's guide for NPSOL 5.0: A Fortran package for nonlinear programming, Report SOL 86-1 (revised July 1998).

1983

• S. T. McCormick (1983), A combinational approach to some sparse matrix problems, Report SOL 83-5, 69 pages.
• P. E. Gill, W. Murray, M. A. Saunders and M. H. Wright (1983), Documentation for FDCALC and FDCORE, Report SOL 83-6, 21 pages.

1980

• G. B. Dantzig (1980), Expected number of steps of the simplex method for a linear program with a convexity constraint, Report SOL 80-3, 34 pages.
• N. Zadeh (1980), What is the worst case behavior of the simplex algorithm?, Report OR 80-27, 28 pages.
• J. R. Birge (1980), Solution methods for stochastic dynamic linear programs, Report SOL 80-29.

1979

• N. Buras (1979), Determining the feasibility of integrating water resource constraints into energy models, Report SOL 79-4, 97 pages.
• R. Fourer (1979), Solving staircase linear programs by the simplex method, 1: Inversion, Report SOL 79-18, 80 pages. In Mathematical Programming 23 (1982) 274-313.

1978

• W. Murray and M. H. Wright (1978), Projected Lagrangian methods based on the trajectories of penalty and barrier functions, Report SOL 78-23, 67 pages.

1977

• T. J. Connolly, G. B. Dantzig, and S. C. Parikh (1977), The Stanford pilot energy/economic model, Report SOL 77-19, 45 pages.
• P. J. Jansen (1977), Decision under several objectives, Report SOL 77-20, 65 pages.

1976

• J. A. Tomlin (1976), A program for solving linear complementarity problems by Lemke's method, Report SOL 76-16, 40 pages.

1975

• M. Kallio and E. L. Porteus (1975), A class of methods for linear programming, Report SOL 75-7, 9 pages.
• J. A. Tomlin (1975), A parametric bounding method for finding a minimum l-infinity-norm solution to a system of equations, Report SOL 75-12, 20 pages.

1974

• C. Winkler (1974), Basis factorization for block-angular linear programs: unified theory of partitioning and decomposition using the simplex method, Report SOL 74-19, 126 pages.