A Comparative Study of Large-Scale Nonlinear Optimization Algorithms

  • Hande Y. Benson
  • David F. Shanno
  • Robert J. Vanderbei
Part of the Applied Optimization book series (APOP, volume 82)


In recent years, much work has been done on implementing a variety of algorithms in nonlinear programming software. In this paper, we analyze the performance of several state-of-the-art optimization codes on large-scale nonlinear optimization problems. Extensive numerical results are presented on different classes of problems, and features of each code that make it efficient or inefficient for each class are examined.


interior-point methods large-scale optimization nonlinear programming 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H.Y. Benson, D.F. Shanno, and R.J. Vanderbei. Interior-point methods for non-convex nonlinear programming: Filter methods and merit functions. Technical Report ORFE 00–06, Department of Operations Research and Financial Engineering, Princeton University, 2000.Google Scholar
  2. [2]
    R.H. Byrd, M.E. Hribar, and J. Nocedal. An interior point algorithm for large scale nonlinear programming. SIAM J. Opt., 9(4):877–900, 1999.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    A.R. Conn, N. Gould, and Ph.L. Toint. Constrained and unconstrained testing environment. Scholar
  4. [4]
    A.R. Conn, N.I.M. Gould, and Ph.L. Toint. LANCELOT: a Fortran Package for Large-Scale Nonlinear Optimization (Release A). Springer Verlag, Heidelberg, New York, 1992.zbMATHGoogle Scholar
  5. [5]
    E. D. Dolan and J. J. Moré. Benchmarking optimization software with COPS. Technical Report ANL/MCS-246, Argonne National Laboratory, November 2000.Google Scholar
  6. [6]
    E. D. Dolan and J. J. Moré. Benchmarking optimization software with performance profiles. Math. Programming, 91:201–214, 2002.zbMATHCrossRefGoogle Scholar
  7. [7]
    R. Fletcher and S. Leyffer. Nonlinear programming without a penalty function. Technical Report NA/171, University of Dundee, Dept. of Mathematics, Dundee, Scotland, 1997.Google Scholar
  8. [8]
    R. Fourer, D.M. Gay, and B.W. Kernighan. AMPL: A Modeling Language for Mathematical Programming. Scientific Press, 1993.Google Scholar
  9. [9]
    P.E. Gill, W. Murray, and M.A. Saunders. User’s guide for SNOPT 5.3: A Fortran package for large-scale nonlinear programming. Technical report, Systems Optimization Laboratory, Stanford University, Stanford, CA, 1997.Google Scholar
  10. [10]
    D.F. Shanno and R.J. Vanderbei. Interior-point methods for nonconvex nonlinear programming: Orderings and higher-order methods. Math. Prog.,87(2):303–316, 2000.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    R.J. Vanderbei. AMPL models. Scholar
  12. [12]
    R.J. Vanderbei. A comparison between the minimum-local-fill and minimum-degree algorithms. Technical report, AT&T Bell Laboratories, 1990.Google Scholar
  13. [13]
    R.J. Vanderbei. Symmetric quasi-definite matrices. SIAM Journal on Optimization, 5(1):100–113, 1995.MathSciNetzbMATHCrossRefGoogle Scholar
  14. [14]
    R.J. Vanderbei. LOQO: An interior point code for quadratic programming. Optimization Methods and Software,12:451–484, 1999.MathSciNetCrossRefGoogle Scholar
  15. [15]
    R.J. Vanderbei and D.F. Shanno. Ari interior-point algorithm for nonconvex nonlinear programming. Computational Optimization and Applications,13:231–252, 1999.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers B.V. 2003

Authors and Affiliations

  • Hande Y. Benson
    • 1
  • David F. Shanno
    • 2
  • Robert J. Vanderbei
    • 1
  1. 1.Operations Research and Financial EngineeringPrinceton UniversityPrincetonUSA
  2. 2.Rutgers UniversityNew BrunswickUSA

Personalised recommendations