Nonlinear Programming and Engineering Applications

  • Robert J. Vanderbei
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 76)


The last decade has seen dramatic strides in ones ability to solve nonlinear programming problems. In this chapter, we review a few applications of nonlinear programming to interesting, and in some cases important, engineering problems.


Linear Programming Problem Simplex Method Filter Coefficient Finite Impulse Response Filter Extrasolar Planet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [1]
    M.P. Bendsøe, A. Ben-Tal, and J. Zowe. Optimization methods for truss geometry and topology design. Structural Optimization, 7: 141–159, 1994.CrossRefGoogle Scholar
  2. [2]
    R. Broucke. New orbits for the n-body problem. In Proceedings of Conference on New Trends in Astrodynamics and Applications, 2003.Google Scholar
  3. [3]
    A. Chenciner, J. Gerver, R. Montgomery, and C. Simó. Simple choreographic motions on n bodies: a preliminary study. In Geometry, Mechanics and Dynamics, 2001.Google Scholar
  4. [4]
    A. Chenciner and R. Montgomery. A remarkable periodic solution of the three-body problem in the case of equal masses. Annals of Math, 152: 881–901, 2000.MathSciNetCrossRefGoogle Scholar
  5. [5]
    J.O. Coleman and D.P. Scholnik. Design of Nonlinear-Phase FIR Filters with Second-Order Cone Programming. In Proceedings of 1999 Midwest Symposium on Circuits and Systems, 1999.Google Scholar
  6. [6]
    J.O. Coleman. Systematic mapping of quadratic constraints on embedded fir filters to linear matrix inequalities. In Proceedings of 1998 Conference on Information Sciences and Systems, 1998.Google Scholar
  7. [7]
    R. Fourer, D.M. Gay, and B.W. Kernighan. AMPL: A Modeling Language for Mathematical Programming. Scientific Press, 1993.Google Scholar
  8. [8]
    J.K. Ho. Optimal design of multi-stage structures: a nested decomposition approach. Computers and Structures, 5: 249–255, 1975.CrossRefGoogle Scholar
  9. [9]
    N.K. Karmarkar. A new polynomial time algorithm for linear programming. Combinatorica, 4: 373–395, 1984.zbMATHMathSciNetGoogle Scholar
  10. [10]
    N.J. Kasdin, R.J. Vanderbei, D.N. Spergel, and M.G. Littman. Extrasolar Planet Finding via Optimal Apodized and Shaped Pupil Coronagraphs. Astrophysical Journal, 582: 1147–1161, 2003.CrossRefGoogle Scholar
  11. [11]
    N. J. Kasdin, D. N. Spergel, and M. G. Littman. An optimal shaped pupil coronagraph for high contrast imaging, planet finding, and spectroscopy. submitted to Applied Optics, 2002.Google Scholar
  12. [12]
    M.S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret. Applications of second-order cone programming. Technical report, Electrical Engineering Department, Stanford University, Stanford, CA 94305, 1998. To appear in Linear Algebra and Applications special issue on linear algebra in control, signals and imaging.Google Scholar
  13. [13]
    I.J. Lustig, R.E. Marsten, and D.F. Shanno. Interior point methods for linear programming: computational state of the art. Operations Research Society of America Journal on Computing, 6: 1–14, 1994.MathSciNetGoogle Scholar
  14. [14]
    C. Moore. Braids in classical gravity. Physical Review Letters, 70: 3675–3679, 1993.zbMATHMathSciNetCrossRefGoogle Scholar
  15. [15]
    D. N. Spergel. A new pupil for detecting extrasolar planets. astro-ph/0101142, 2000.Google Scholar
  16. [16]
    R.J. Vanderbei and D.F. Shanno. An interior-point algorithm for nonconvex nonlinear programming. Computational Optimization and Applications, 13: 231–252, 1999.MathSciNetCrossRefGoogle Scholar
  17. [17]
    R.J. Vanderbei, D.N. Spergel, and N.J. Kasdin. Circularly Symmetric Apodization via Starshaped Masks. Astrophysical Journal, 599: 686–694, 2003.CrossRefGoogle Scholar
  18. [18]
    R.J. Vanderbei, D.N. Spergel, and N.J. Kasdin. Spiderweb Masks for High Contrast Imaging. Astrophysical Journal, 590: 593–603, 2003.CrossRefGoogle Scholar
  19. [19]
    R.J. Vanderbei. LOQO user’s manual-version 3.10. Optimization Methods and Software, 12: 485–514, 1999.zbMATHMathSciNetGoogle Scholar
  20. [20]
    R.J. Vanderbei., 2001.Google Scholar
  21. [21]
    R.J. Vanderbei. Linear Programming: Foundations and Extensions. Kluwer Academic Publishers, 2nd edition, 2001.Google Scholar
  22. [22]
    S.-P. Wu, S. Boyd, and L. Vandenberghe. Magnitude filter design via spectral factorization and convex optimization. Applied and Computational Control, Signals and Circuits, 1997. To appear.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Robert J. Vanderbei
    • 1
  1. 1.Operations Research and Financial Engineering DepartmentPrinceton UniversityUSA

Personalised recommendations