Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. Abbot,Tricks of the trade, The Mathematica Journal3 (1993), 18–22.
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.
N. Blachman,Mathematica: A Practical Approach Englewood Cliffs, New Jersey: Prentice-Hall, (1992).
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.
J. C. Culioli, “Optimization with Mathematica.”In:Computational Economics and Finance (H. Varian, ed), Telos/Springer-Verlag, Santa Clara CA, (1996).
M. Frank and P. Wolfe,An algorithm for quadratic programming, Naval Res. Logistics Quart.,3 (1956), 95–110.
T. Gray and J. Glynn,Exploring Mathematics in Mathematica, Redwood City, California: Adisson-Wesley, (1991).
D. M. Himellblau,Applied Nonlinear Programming, McGraw-Hill Book Company, (1972).
M. Iri and K. Kubota,Norms, rounding errors, partial derivatives and fast automatic differentiation, IECE Transactions,74 (1991), 463–471.
S. L. S. Jacoby, J. S. Kowalik and J. T. Pizzo,Iterative methods for nonlinear optimization problems, Prentice-Hall, Inc, Englewood, New Jersey, (1977).
R. Maeder,Programming in Mathematica, Third Edition, Redwood City, California: Adisson-Wesley, (1996).
Stanimirović, P. and Rančić, S.,Implementation of penalty function methods in LISP, Acta Mathematica et Informatica Universitatis Ostraviensis, (1991).
C. Smith and N. Blachman,The Mathematica Graphics Guidebook, Addison-Wesley Publishing Company, Reading, Massachusetts (1995).
S. Wolfram,Mathematica: a system for doing mathematics by computer, Addison-Wesley Publishing Co, Redwood City, California, (1991).
S. Wolfram,Mathematica Book, Version 3.0, Wolfram Media and Cambridge University Press, (1996).
Author information
Authors and Affiliations
Corresponding author
Additional information
Predrag Stanimirović received Ph. D. at University of Niš, Faculty of Science, Department of Mathematics. Since 1996 he works as assistant professor, since 1999 as Assocoiate Professor and since 2003 as full professor. He is a reviewer for Mathematical Reviews. His research interest is in the following areas: generalized inverses (MSC 15A09), symbolic computation (MSC 68Q40) and linear and non-linear programming (MSC 90C05 and 90C30).
Milan Tasić received Ph. D. at University of Niš, Faculty of Science, Department of Mathematics. Since 2003 he works as assistant Professor. His research speciality is mainly the symbolic computation (MSC 68Q40).
Rights and permissions
About this article
Cite this article
Stanimirović, P.S., Tasić, M.B. A modification of gradient method of convex programming and its implementation. JAMC 16, 91–104 (2004). https://doi.org/10.1007/BF02936153
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02936153