## 抄録

The ℓ _{p}-constrained least squares, which is denoted by (Pc), for 0 < p < 1 is addressed. A maximal continuous curve of its critical solutions β(c) for different bounds c forms a critical path which can be constructed with the variational method. The path is a piecewise smooth single-valued function of c, containing non-optimal points such as saddle points and local maxima in general as well as global minima. The path of global minima may coincide with a critical path but may jump from a critical path to another one. The breakpoints of the greedy path (a critical path constructed with a certain greedy selection criterion) coincide with the step-by-step solutions generated by the orthogonal matching pursuit (OMP). A critical point of (Pc) is also a critical point of the ℓ _{p}-penalized least squares (Q _{λ}) which reformulates (P _{c}) with the Lagrangian multiplier. The greedy path is a multi-valued function of λ and is formed by a collection of multiple critical paths of (Q _{λ}).

本文言語 | English |
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ホスト出版物のタイトル | 2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012 |

ページ | 2221-2225 |

ページ数 | 5 |

DOI | |

出版ステータス | Published - 2012 10月 22 |

外部発表 | はい |

イベント | 2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States 継続期間: 2012 7月 1 → 2012 7月 6 |

### 出版物シリーズ

名前 | IEEE International Symposium on Information Theory - Proceedings |
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### Other

Other | 2012 IEEE International Symposium on Information Theory, ISIT 2012 |
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国/地域 | United States |

City | Cambridge, MA |

Period | 12/7/1 → 12/7/6 |

## ASJC Scopus subject areas

- 理論的コンピュータサイエンス
- 情報システム
- モデリングとシミュレーション
- 応用数学

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