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Non-linear programming

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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 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://www.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