# Non-linear programming

From Encyclopedia of Mathematics

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) |

#### Comments

#### References

[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