Computational Management Science

, Volume 7, Issue 4, pp 437–463 | Cite as

DrAmpl: a meta solver for optimization problem analysis

Original Paper


Optimization problems modeled in the AMPL modeling language (Fourer et al., in AMPL: a modeling language for mathematical programming, 2002) may be examined by a set of tools found in the AMPL Solver Library (Gay, in Hooking your solver to AMPL, 1997). DrAmpl is a meta solver which, by use of the AMPL Solver Library, dissects such optimization problems, obtains statistics on their data, is able to symbolically prove or numerically disprove convexity of the functions involved and provides aid in the decision for an appropriate solver. A problem is associated with a number of relevant solvers available on the NEOS Server for Optimization (Czyzyk et al., in IEEE J Comput Sci Eng 5:68–75, 1998) by means of a relational database. We describe the need for such a tool, the design of DrAmpl and some of its consequences, and keep in mind that a similar tool could be developed for other algebraic modeling languages.


Optimization model AMPL modeling language Directed acyclic graph Convexity assessment Structural model analysis Solver recommendation 

JEL Classification

C61 C63 

Mathematics Subject Classification (2000)

90C25 90C26 90C30 


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  1. Bauer FL (1974) Computational graphs and rounding error. SIAM J Numer Anal 11(1): 87–96CrossRefGoogle Scholar
  2. Brooke A, Kendrick D, Meeraus A (1998) GAMS: a users’ guide. GAMS Development Corporation, WashingtonGoogle Scholar
  3. Byrd RH, Gilbert J-Ch, Nocedal J (2000) A trust region method based on interior point techniques for nonlinear programming. Math Program Ser A 89(1): 149–185CrossRefGoogle Scholar
  4. Byrd RH, Gould NIM, Nocedal J, Waltz RA (2006) On the convergence of successive linear-quadratic programming algorithms. SIAM J Optim 16(2): 471–489CrossRefGoogle Scholar
  5. Chinneck J (2001) Analyzing mathematical programs using MProbe. Ann Oper Res 104: 33–48CrossRefGoogle Scholar
  6. Conn AR, Gould NIM, Toint PL (1992) LANCELOT, a Fortran package for large-scale nonlinear optimization (Release A). Number 17 in Springer Series in Computational Mathematics. Springer-Verlag, New YorkGoogle Scholar
  7. Czyzyk J, Mesnier M, Moré JJ (1998) The NEOS server. IEEE J Comput Sci Eng 5: 68–75CrossRefGoogle Scholar
  8. Dolan E (2001) The NEOS server 4.0 administrative guide. Technical Memorandum ANL/MCS-TM-250, The Mathematical and Computer Science Division, Argonne National Laboratory, Argonne, ILGoogle Scholar
  9. Dolan ED, Moré JJ (2001a) Benchmarking optimization software with COPS. Technical Report ANL/MCS-246, Argonne National LaboratoryGoogle Scholar
  10. Dolan ED, Moré JJ (2001b)
  11. Fletcher R, Gould NIM, Leyffer S, Toint PL, Wächter A (2002) On the global convergence of trust-region SQP-filter algorithms for general nonlinear programming. SIAM J Optim 13(2): 635–659CrossRefGoogle Scholar
  12. Fourer R, Gay DM, Kernighan BW (2002) AMPL: a modeling language for mathematical programming, 2nd edn. Duxbury PressGoogle Scholar
  13. Fourer R, Maheshwari C, Neumaier A, Orban D, Schichl H (2009) Convexity and concavity detection in computational graphs: tree walks for convexity proving. INFORMS J Comput. doi:10.1287/ijoc.1090.0321 (Published online ahead of print)
  14. Gay DM (1991) Automatic differentiation of nonlinear AMPL models. In: Griewank A, Corliss G (eds) Automatic differentiation of algorithms: theory, implementation, and application. SIAM, Philadelphia, pp 61–73Google Scholar
  15. Gay DM (1996a) Automatically finding and exploiting partially separable structure in nonlinear programming problems. Numerical Analysis Manuscript. AT&T Bell LaboratoriesGoogle Scholar
  16. Gay DM (1996) More AD of nonlinear AMPL models: computing Hessian information and exploiting partial separability. In: Corliss G, Berz M, Bischof C, Griewank A (eds) Computational differentiation: techniques, applications and tools. SIAM, Philadelphia, pp 173–184Google Scholar
  17. Gay DM (1997) Hooking your solver to AMPL. Technical Report 97-4-06. Lucent Technologies Bell Labs Innovations, Murray Hill, NJ.
  18. Gill P, Murray W, Saunders M (1997) User’s guide for SNOPT 5.3: a Fortran package for large-scale nonlinear programming. Regents of the University of California, Board of Trustees of Stanford UniversityGoogle Scholar
  19. Gould NIM, Lucidi S, Roma M, Toint PL (1999) Solving the trust-region subproblem using the Lanczos method. SIAM J Optim 9(2): 504–525CrossRefGoogle Scholar
  20. Grant MC, Boyd S, Ye Y (2006) Disciplined convex programming. In: Liberti L, Maculan N (eds) Global optimization: from theory to implementation, nonconvex optimization and its applications. Springer, New York, pp 155–210Google Scholar
  21. Griewank A (2000) Evaluating derivatives: principles and techniques of algorithmic differentiation. Number FR19 in Frontiers in Applied Mathematics. SIAMGoogle Scholar
  22. Gropp W, Moré JJ (1997) Optimization environments and the NEOS server. In: Buhmann MD, Iserles A (eds) Approximation theory and optimization. Cambridge University Press, Cambridge, pp 167–182Google Scholar
  23. Kantorovich LV (1957) On a mathematical symbolism convenient for performing machine calculations. Dokl Akad Nauk SSSR 113(4): 738–741 (in Russian)Google Scholar
  24. Nenov IP, Fylstra DH, Kolev LV (2004) Convexity determination in the microsoft excel solver using automatic differentiation techniques. Technical Report, Frontline Systems Inc., Incline Village NV, USAGoogle Scholar
  25. Schichl H, Neumaier A (2005) Interval analysis on directed acyclic graphs for global optimization. J Glob Optim 33(4): 541–562CrossRefGoogle Scholar
  26. Spellucci P (1998) An SQP method for general nonlinear programs using only equality constrained subproblems. Math Program 82(3): 413–448CrossRefGoogle Scholar
  27. Vanderbei RJ, Shanno DF (1999) An interior point algorithm for nonconvex nonlinear programming. Comput Optim Appl 13(3): 231–252CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Industrial Engineering and Management SciencesNorthwestern UniversityEvanstonUSA
  2. 2.Département de Mathématiques et Génie IndustrielGERAD and École Polytechnique de MontréalMontrealCanada

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