A modification of gradient method of convex programming and its implementation



A modification of the gradient method of convex programming is introduced. Also, we describe symbolic implementation of the gradient method and its modification by means of the programming language MATHEMATICA. A few numerical examples are reported.

AMS Mathematics Subject Classification

90C30 68N15 

Key words and phrases

Convex optimization gradient method symbolic processing MATHEMATICA 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. Abbot,Tricks of the trade, The Mathematica Journal3 (1993), 18–22.Google Scholar
  2. 2.
    H. Basirzadeh, A. V. Kamyad and S. Effati,An approach for solving nonlinear programming problems, J. Appl. Math. & Computing (old: KJCAM)9(2) (2002), 547–561.MATHMathSciNetGoogle Scholar
  3. 3.
    N. Blachman,Mathematica: A Practical Approach Englewood Cliffs, New Jersey: Prentice-Hall, (1992).MATHGoogle Scholar
  4. 4.
    M. Cocan and B. Pop,An algorithm for solving the problem of convex programming with several objective functions, J. Appl. Math. & Computing(old: KJCAM)6(1) (1999), 79–89.MATHMathSciNetGoogle Scholar
  5. 5.
    J. C. Culioli, “Optimization with Mathematica.”In:Computational Economics and Finance (H. Varian, ed), Telos/Springer-Verlag, Santa Clara CA, (1996).Google Scholar
  6. 6.
    M. Frank and P. Wolfe,An algorithm for quadratic programming, Naval Res. Logistics Quart.,3 (1956), 95–110.CrossRefMathSciNetGoogle Scholar
  7. 7.
    T. Gray and J. Glynn,Exploring Mathematics in Mathematica, Redwood City, California: Adisson-Wesley, (1991).Google Scholar
  8. 8.
    D. M. Himellblau,Applied Nonlinear Programming, McGraw-Hill Book Company, (1972).Google Scholar
  9. 9.
    M. Iri and K. Kubota,Norms, rounding errors, partial derivatives and fast automatic differentiation, IECE Transactions,74 (1991), 463–471.Google Scholar
  10. 10.
    S. L. S. Jacoby, J. S. Kowalik and J. T. Pizzo,Iterative methods for nonlinear optimization problems, Prentice-Hall, Inc, Englewood, New Jersey, (1977).Google Scholar
  11. 11.
    R. Maeder,Programming in Mathematica, Third Edition, Redwood City, California: Adisson-Wesley, (1996).Google Scholar
  12. 12.
    Stanimirović, P. and Rančić, S.,Implementation of penalty function methods in LISP, Acta Mathematica et Informatica Universitatis Ostraviensis, (1991).Google Scholar
  13. 13.
    C. Smith and N. Blachman,The Mathematica Graphics Guidebook, Addison-Wesley Publishing Company, Reading, Massachusetts (1995).Google Scholar
  14. 14.
    S. Wolfram,Mathematica: a system for doing mathematics by computer, Addison-Wesley Publishing Co, Redwood City, California, (1991).Google Scholar
  15. 15.
    S. Wolfram,Mathematica Book, Version 3.0, Wolfram Media and Cambridge University Press, (1996).Google Scholar

Copyright information

© Korean Society for Computational and Applied Mathematics 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Niš, Faculty of ScienceNišSerbia and Montenegro

Personalised recommendations