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

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
Title of host publicationOptimization of Complex Systems
Subtitle of host publicationTheory, Models, Algorithms and Applications, 2019
EditorsHoai An Le Thi, Hoai Minh Le, Tao Pham Dinh
PublisherSpringer Verlag
Pages221-227
Number of pages7
ISBN (Print)9783030218027
DOIs
Publication statusPublished - 2020 Jan 1
Event6th World Congress on Global Optimization, WCGO 2019 - Metz, France
Duration: 2019 Jul 82019 Jul 10

Publication series

NameAdvances in Intelligent Systems and Computing
Volume991
ISSN (Print)2194-5357

Conference

Conference6th World Congress on Global Optimization, WCGO 2019
CountryFrance
CityMetz
Period19-07-0819-07-10

Fingerprint

Polynomials

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science(all)

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
Nguyen, Huu Quang ; Sheu, Ruey-Lin ; Xia, Yong. / Solving a Type of the Tikhonov Regularization of the Total Least Squares by a New S-Lemma. Optimization of Complex Systems: Theory, Models, Algorithms and Applications, 2019. editor / Hoai An Le Thi ; Hoai Minh Le ; Tao Pham Dinh. Springer Verlag, 2020. pp. 221-227 (Advances in Intelligent Systems and Computing).
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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.",
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Nguyen, HQ, Sheu, R-L & 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 proceedingConference contribution

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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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Nguyen HQ, Sheu R-L, Xia Y. Solving a Type of the Tikhonov Regularization of the Total Least Squares by a New S-Lemma. In Le Thi HA, Le HM, Pham Dinh T, editors, Optimization of Complex Systems: Theory, Models, Algorithms and Applications, 2019. Springer Verlag. 2020. p. 221-227. (Advances in Intelligent Systems and Computing). https://doi.org/10.1007/978-3-030-21803-4_23