### Abstract

We consider the convex feasibility problem, which is to determine a point in the intersection of a finite number of closed convex sets. It was shown in the past literature a so-called generalized acceleration method converges to a feasible point in the intersection of all the sets, assuming the intersection set has a nonempty interior. In this letter, we establish the same convergence result without any assumption on the interior of the feasible set. In particular, we devise a randomized accelerated projection algorithm and prove its linear convergence rate when all the convex sets are half-spaces in a finite-dimensional Euclidean space. Numerical experiments comparing the generalized acceleration method with the classic cyclic projection methods are presented, which justify the fast convergence rate and the out-performance of the proposed algorithm.

Original language | English (US) |
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Article number | 9113702 |

Pages (from-to) | 85-90 |

Number of pages | 6 |

Journal | IEEE Control Systems Letters |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2021 |

### Keywords

- Successive projection method
- convex feasibility
- convex optimization

### ASJC Scopus subject areas

- Control and Systems Engineering
- Control and Optimization

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## Cite this

*IEEE Control Systems Letters*,

*5*(1), 85-90. [9113702]. https://doi.org/10.1109/LCSYS.2020.3000714