### Abstract

This paper extends and analyzes a new potential reduction algorithm for solving smooth convex programming. Under a kind of strict feasibility assumption, we show that the algorithm under modification requires a total of O((ρ - n)ℓ) number of iterations, and the total arithmetic operations are not more than O(n^{3}ℓ), where n + √2n ≤ ρ ≤ 2n and ℓ is the initial input size. As an application to usual linear or convex quadratic programming, this algorithm solves the pair of primal and dual problems in at most O((ρ - n)L) iterations, and the total arithmetic operations are shown to be of the order of O(n^{3}L), where L is the input size.

Original language | English |
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Pages (from-to) | 235-262 |

Number of pages | 28 |

Journal | Optimization |

Volume | 44 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1998 Jan 1 |

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### Keywords

- Arithmetic operation
- Potential reduction algorithm
- Smooth convex programming
- Strict feasibility

### ASJC Scopus subject areas

- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics