# Convex programming

From Encyclopedia of Mathematics

2010 Mathematics Subject Classification: *Primary:* 90C25 [MSN][ZBL]

The branch of mathematical programming dealing with the theory and methods of solving problems of minimization of convex functions on convex sets defined by systems of equalities and inequalities. There exists a quite complete theory of convex programming, and numerous methods have been developed for solving problems in this field. A priori estimates of convergence have been established for many iterative methods of convex programming. Quadratic programming is a branch of convex programming.

#### References

[1] | I.I. Eremin, N.N. Astaf'ev, "Introduction to the theory of linear and convex programming" , Moscow (1976) (In Russian) |

[2] | V.G. Karmanov, "Mathematical programming" , Moscow (1975) (In Russian) |

[3] | W.I. Zangwill, "Nonlinear programming: a unified approach" , Prentice-Hall (1969) |

[4] | E. Polak, "Computational methods in optimization: a unified approach" , Acad. Press (1971) |

[5] | R.T. Rockafellar, "Convex analysis" , Princeton Univ. Press (1970) |

[6] | J. Stoer, C. Witzgall, "Convexity and optimization in finite dimensions" , 1 , Springer (1970) |

[7] | S.P. Boyd, L. Vandenberghe, "Convex Optimization" , Cambridge University Press (2004). DOI 10.1017/CBO9780511804441 |

**How to Cite This Entry:**

Convex programming.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Convex_programming&oldid=38777

This article was adapted from an original article by V.G. Karmanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article