### Abstract

We present a new S-lemma with two quadratic equalities and use it to minimize a special type of polynomials of degree 4. As a result, by the Dinkelbach approach with 2 SDP’s (semidefinite programming), the minimum value and the minimum solution to the Tikhonov regularization of the total least squares problem with can be nicely obtained.

Original language | English |
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Title of host publication | Optimization of Complex Systems |

Subtitle of host publication | Theory, Models, Algorithms and Applications, 2019 |

Editors | Hoai An Le Thi, Hoai Minh Le, Tao Pham Dinh |

Publisher | Springer Verlag |

Pages | 221-227 |

Number of pages | 7 |

ISBN (Print) | 9783030218027 |

DOIs | |

Publication status | Published - 2020 Jan 1 |

Event | 6th World Congress on Global Optimization, WCGO 2019 - Metz, France Duration: 2019 Jul 8 → 2019 Jul 10 |

### Publication series

Name | Advances in Intelligent Systems and Computing |
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Volume | 991 |

ISSN (Print) | 2194-5357 |

### Conference

Conference | 6th World Congress on Global Optimization, WCGO 2019 |
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Country | France |

City | Metz |

Period | 19-07-08 → 19-07-10 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Computer Science(all)

### Cite this

*Optimization of Complex Systems: Theory, Models, Algorithms and Applications, 2019*(pp. 221-227). (Advances in Intelligent Systems and Computing; Vol. 991). Springer Verlag. https://doi.org/10.1007/978-3-030-21803-4_23

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*Optimization of Complex Systems: Theory, Models, Algorithms and Applications, 2019.*Advances in Intelligent Systems and Computing, vol. 991, Springer Verlag, pp. 221-227, 6th World Congress on Global Optimization, WCGO 2019, Metz, France, 19-07-08. https://doi.org/10.1007/978-3-030-21803-4_23

**Solving a Type of the Tikhonov Regularization of the Total Least Squares by a New S-Lemma.** / Nguyen, Huu Quang; Sheu, Ruey Lin; Xia, Yong.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Solving a Type of the Tikhonov Regularization of the Total Least Squares by a New S-Lemma

AU - Nguyen, Huu Quang

AU - Sheu, Ruey Lin

AU - Xia, Yong

PY - 2020/1/1

Y1 - 2020/1/1

N2 - We present a new S-lemma with two quadratic equalities and use it to minimize a special type of polynomials of degree 4. As a result, by the Dinkelbach approach with 2 SDP’s (semidefinite programming), the minimum value and the minimum solution to the Tikhonov regularization of the total least squares problem with can be nicely obtained.

AB - We present a new S-lemma with two quadratic equalities and use it to minimize a special type of polynomials of degree 4. As a result, by the Dinkelbach approach with 2 SDP’s (semidefinite programming), the minimum value and the minimum solution to the Tikhonov regularization of the total least squares problem with can be nicely obtained.

UR - http://www.scopus.com/inward/record.url?scp=85068401377&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068401377&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-21803-4_23

DO - 10.1007/978-3-030-21803-4_23

M3 - Conference contribution

AN - SCOPUS:85068401377

SN - 9783030218027

T3 - Advances in Intelligent Systems and Computing

SP - 221

EP - 227

BT - Optimization of Complex Systems

A2 - Le Thi, Hoai An

A2 - Le, Hoai Minh

A2 - Pham Dinh, Tao

PB - Springer Verlag

ER -