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Difference between revisions of "Non-linear programming"

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The branch of [[Mathematical programming|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).
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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 [[Convex programming|convex programming]], the problems in which are characterized by the fact that every local minimum point is a global minimum.
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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====
 
<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></table>
 
 
 
 
 
 
 
====Comments====
 
 
 
  
 
====References====
 
====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  M. Minoux,  "Mathematical programming: theory and algorithms" , Wiley  (1986)</TD></TR></table>
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<table>
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<TR><TD valign="top">[1]</TD> <TD valign="top">  W.I. Zangwill,  "Nonlinear programming: a unified approach" , Prentice-Hall  (1969)</TD></TR>
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<TR><TD valign="top">[2]</TD> <TD valign="top">  V.G. Karmanov,  "Mathematical programming" , Moscow  (1975)  (In Russian)</TD></TR>
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<TR><TD valign="top">[3]</TD> <TD valign="top">  E. Polak,  "Computational methods in optimization: a unified approach" , Acad. Press  (1971)</TD></TR>
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  M. Minoux,  "Mathematical programming: theory and algorithms" , Wiley  (1986)</TD></TR>
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</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=11270
This article was adapted from an original article by V.G. Karmanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article