Difference between revisions of "Non-linear programming"
From Encyclopedia of Mathematics
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| − | The branch of [[ | + | {{TEX|done}} |
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| + | The branch of [[mathematical programming]] concerned with the theory and methods for solving problems of optimization of non-linear functions on sets given by non-linear constraints (equalities and inequalities). | ||
The principal difficulty in solving problems in non-linear programming is their multi-extremal nature, while the known numerical methods for solving them in the general case guarantee convergence of minimizing sequences to local extremum points only. | The principal difficulty in solving problems in non-linear programming is their multi-extremal nature, while the known numerical methods for solving them in the general case guarantee convergence of minimizing sequences to local extremum points only. | ||
| − | The best studied branch of non-linear programming is [[ | + | The best studied branch of non-linear programming is [[convex programming]], the problems in which are characterized by the fact that every local minimum point is a global minimum. |
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====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Minoux, "Mathematical programming: theory and algorithms" , Wiley (1986)</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[1]</TD> <TD valign="top"> W.I. Zangwill, "Nonlinear programming: a unified approach" , Prentice-Hall (1969)</TD></TR> | ||
| + | <TR><TD valign="top">[2]</TD> <TD valign="top"> V.G. Karmanov, "Mathematical programming" , Moscow (1975) (In Russian)</TD></TR> | ||
| + | <TR><TD valign="top">[3]</TD> <TD valign="top"> E. Polak, "Computational methods in optimization: a unified approach" , Acad. Press (1971)</TD></TR> | ||
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Minoux, "Mathematical programming: theory and algorithms" , Wiley (1986)</TD></TR> | ||
| + | </table> | ||
Latest revision as of 08:52, 25 April 2016
The branch of mathematical programming concerned with the theory and methods for solving problems of optimization of non-linear functions on sets given by non-linear constraints (equalities and inequalities).
The principal difficulty in solving problems in non-linear programming is their multi-extremal nature, while the known numerical methods for solving them in the general case guarantee convergence of minimizing sequences to local extremum points only.
The best studied branch of non-linear programming is convex programming, the problems in which are characterized by the fact that every local minimum point is a global minimum.
References
| [1] | W.I. Zangwill, "Nonlinear programming: a unified approach" , Prentice-Hall (1969) |
| [2] | V.G. Karmanov, "Mathematical programming" , Moscow (1975) (In Russian) |
| [3] | E. Polak, "Computational methods in optimization: a unified approach" , Acad. Press (1971) |
| [a1] | M. Minoux, "Mathematical programming: theory and algorithms" , Wiley (1986) |
How to Cite This Entry:
Non-linear programming. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Non-linear_programming&oldid=38638
Non-linear programming. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Non-linear_programming&oldid=38638
This article was adapted from an original article by V.G. Karmanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article