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

Huu Quang Nguyen; Ruey Lin Sheu; Yong Xia

doi: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

Huu Quang Nguyen, Ruey Lin Sheu, Yong Xia

Department of Mathematics

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

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
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	https://doi.org/10.1007/978-3-030-21803-4_23
Publication status	Published - 2020
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
Volume	991
ISSN (Print)	2194-5357
ISSN (Electronic)	2194-5365

Conference

Conference	6th World Congress on Global Optimization, WCGO 2019
Country/Territory	France
City	Metz
Period	19-07-08 → 19-07-10

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science(all)

Access to Document

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

Cite this

Nguyen, H. Q., Sheu, R. L., & Xia, Y. (2020). Solving a Type of the Tikhonov Regularization of the Total Least Squares by a New S-Lemma. In H. A. Le Thi, H. M. Le, & T. Pham Dinh (Eds.), 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

@inproceedings{0937e7396e0f43829c951afb0dad03a0,

title = "Solving a Type of the Tikhonov Regularization of the Total Least Squares by a New S-Lemma",

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{\textquoteright}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.",

author = "Nguyen, {Huu Quang} and Sheu, {Ruey Lin} and Yong Xia",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.; 6th World Congress on Global Optimization, WCGO 2019 ; Conference date: 08-07-2019 Through 10-07-2019",

year = "2020",

doi = "10.1007/978-3-030-21803-4_23",

language = "English",

isbn = "9783030218027",

series = "Advances in Intelligent Systems and Computing",

publisher = "Springer Verlag",

pages = "221--227",

editor = "{Le Thi}, {Hoai An} and Le, {Hoai Minh} and {Pham Dinh}, Tao",

booktitle = "Optimization of Complex Systems",

address = "Germany",

}

Nguyen, HQ, Sheu, RL & Xia, Y 2020, Solving a Type of the Tikhonov Regularization of the Total Least Squares by a New S-Lemma. in HA Le Thi, HM Le & T Pham Dinh (eds), 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.
Optimization of Complex Systems: Theory, Models, Algorithms and Applications, 2019. ed. / Hoai An Le Thi; Hoai Minh Le; Tao Pham Dinh. Springer Verlag, 2020. p. 221-227 (Advances in Intelligent Systems and Computing; Vol. 991).

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

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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

Y1 - 2020

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.

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T3 - Advances in Intelligent Systems and Computing

SP - 221

EP - 227

BT - Optimization of Complex Systems

A2 - Le Thi, Hoai An

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PB - Springer Verlag

T2 - 6th World Congress on Global Optimization, WCGO 2019

Y2 - 8 July 2019 through 10 July 2019

ER -

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

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