Advertisement

General Solution Methods for Constrained Optimization

  • H. A. Eiselt
  • Carl-Louis Sandblom
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 282)

Abstract

In Chap.  1 we dealt with optimality conditions for unconstrained problems, and then we described a number of algorithms for such problems in Chap.  2. The previous chapter discussed optimality conditions for constrained problems, and in parallel fashion, we will now turn to algorithms for such optimization problems. This chapter will cover some general approaches for constrained optimization, and the following three chapters describe some of the many algorithms for specific types of problems.

References

  1. Bazaraa MS, Sherali HD, Shetty CM (2013) Nonlinear programming: theory and algorithms. (3rd ed.) Wiley, New YorkzbMATHGoogle Scholar
  2. Bertsekas DP (2016) Nonlinear programming. (3rd ed.) Athena Scientific, Belmont, MAzbMATHGoogle Scholar
  3. Carroll CW (1961) The created response surface technique for optimizing nonlinear restrained systems. Operations Research 9: 169-184.MathSciNetCrossRefGoogle Scholar
  4. Cottle RW, Thapa MN (2017) Linear and nonlinear optimization. Springer-Verlag, Berlin-Heidelberg-New YorkCrossRefGoogle Scholar
  5. Dantzig GB, Thapa MN (2003) Linear programming 2: theory and extensions. Springer, New York, Berlin, HeidelbergzbMATHGoogle Scholar
  6. Eiselt HA, Sandblom C-L (2007) Linear programming and its applications. Springer-Verlag, Berlin-HeidelbergzbMATHGoogle Scholar
  7. Everett H (1963) Generalized Lagrange multiplier method for solving problems of optimum allocation of resources. Operations Research 11: 399-417MathSciNetCrossRefGoogle Scholar
  8. Fiacco AV, McCormick GP (1964a) Computational algorithm for the sequential unconstrained minimization technique for nonlinear programming. Management Science 10: 601-617CrossRefGoogle Scholar
  9. Fiacco AV, McCormick GP (1964b) The sequential unconstrained minimization technique for nonlinear programming-a primal-dual method. Management Science 10: 360-366CrossRefGoogle Scholar
  10. Fiacco AV, McCormick GP (1966) Extensions of SUMT for nonlinear programming equality constraints and extrapolation. Management Science 12: 816-828MathSciNetCrossRefGoogle Scholar
  11. Fiacco AV, McCormick GP (1967a) The sequential unconstrained minimization technique (SUMT) without parameters. Operations Research 15: 820-827MathSciNetCrossRefGoogle Scholar
  12. Fiacco AV, McCormick GP (1967b) The slacked unconstrained minimization technique for convex programming. The SIAM Journal of Applied Mathematics 15: 505-515MathSciNetCrossRefGoogle Scholar
  13. Fiacco AV, McCormick GP (1968) Nonlinear programming. J. Wiley & Sons, New YorkzbMATHGoogle Scholar
  14. Frisch KR (1956) La résolution des problèmes de programme lineaire pour la méthode du potential logarithmique. Cahiers du seminaire d’Économetrie 4: 7-20Google Scholar
  15. Luenberger DL, Ye Y (2008) Linear and nonlinear programming. (3rd ed.) Springer-Verlag, Berlin-Heidelberg-New YorkCrossRefGoogle Scholar
  16. Rockafellar RT (1970) Convex analysis. University Press, Princeton, NJCrossRefGoogle Scholar
  17. Sandblom C-L (1974) On the convergence of SUMT. Mathematical Programming 6: 360-364MathSciNetCrossRefGoogle Scholar
  18. Sun W, Yuan Y (2006) Optimization theory and methods. Nonlinear programming. Springer-Verlag, Berlin-Heidelberg-New YorkzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • H. A. Eiselt
    • 1
  • Carl-Louis Sandblom
    • 2
  1. 1.Faculty of ManagementUniversity of New BrunswickFrederictonCanada
  2. 2.Department of Industrial EngineeringDalhousie UniversityHalifaxCanada

Personalised recommendations