### Abstract

We present a unified framework for solving linear and convex quadratic programs via interior point methods. At each iteration, this method solves an indefinite system whose matrix is {Mathematical expression} instead of reducing to obtain the usual AD^{2}A^{T} system. This methodology affords two advantages: (1) it avoids the fill created by explicitly forming the product AD^{2}A^{T} when A has dense columns; and (2) it can easily be used to solve nonseparable quadratic programs since it requires only that D be symmetric. We also present a procedure for converting nonseparable quadratic programs to separable ones which yields computational savings when the matrix of quadratic coefficients is dense.

Original language | English (US) |
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Pages (from-to) | 1-32 |

Number of pages | 32 |

Journal | Mathematical Programming |

Volume | 58 |

Issue number | 1-3 |

DOIs | |

State | Published - Jan 1 1993 |

### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)

### Keywords

- Interior point method
- linear programming
- quadratic programming

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## Cite this

*Mathematical Programming*,

*58*(1-3), 1-32. https://doi.org/10.1007/BF01581257