## Abstract

An interior point method is developed for maximizing a concave quadratic function order convex quadratic constraints. The algorithm constructs a sequence of nested convex sets and finds their approximate centers using a partial Newton step. Given the first convex set and its approximate center, the total arithmetic operations required to converge to an approximate solution are of order O(√m(m + n)n^{2} ln ε), where m is the number of constraints, n is the number of variables, and ε is determined by the desired tolerance of the optimal value and the size of the first convex set. A method to initialize the algorithm is also proposed so that the algorithm can start from an arbitrary (perhaps infeasible) point.

Original language | English (US) |
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Pages (from-to) | 529-544 |

Number of pages | 16 |

Journal | SIAM Journal on Numerical Analysis |

Volume | 28 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1991 |

## ASJC Scopus subject areas

- Numerical Analysis