IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v87y2023i2d10.1007_s10898-022-01188-2.html
   My bibliography  Save this article

A facial reduction approach for the single source localization problem

Author

Listed:
  • He Shi

    (Beijing Institute of Technology)

  • Qingna Li

    (Beijing Institute of Technology/Key Laboratory of Mathematical Theory and Computation in Information Security)

Abstract

The single source localization problem (SSLP) appears in several fields such as signal processing and global positioning systems. The optimization problem of SSLP is nonconvex and difficult to find its globally optimal solution. It can be reformulated as a rank constrained Euclidean distance matrix (EDM) completion problem with a number of equality constraints. In this paper, we propose a facial reduction approach to solve such an EDM completion problem. For the constraints of fixed distances between sensors, we reduce them to a face of the EDM cone and derive the closed formulation of the face. We prove constraint nondegeneracy for each feasible point of the resulting EDM optimization problem without a rank constraint, which guarantees the quadratic convergence of semismooth Newton’s method. To tackle the nonconvex rank constraint, we apply the majorized penalty approach developed by Zhou et al. (IEEE Trans Signal Process 66(3):4331-4346, 2018). Numerical results verify the fast speed of the proposed approach while giving comparable quality of solutions as other methods.

Suggested Citation

  • He Shi & Qingna Li, 2023. "A facial reduction approach for the single source localization problem," Journal of Global Optimization, Springer, vol. 87(2), pages 831-855, November.
    • Handle: RePEc:spr:jglopt:v:87:y:2023:i:2:d:10.1007_s10898-022-01188-2
    DOI: 10.1007/s10898-022-01188-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-022-01188-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-022-01188-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. J. Kruskal, 1964. "Nonmetric multidimensional scaling: A numerical method," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 115-129, June.
    2. Stefan Sremac & Fei Wang & Henry Wolkowicz & Lucas Pettersson, 2019. "Noisy Euclidean distance matrix completion with a single missing node," Journal of Global Optimization, Springer, vol. 75(4), pages 973-1002, December.
    3. Defeng Sun, 2006. "The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 761-776, November.
    4. Gale Young & A. Householder, 1938. "Discussion of a set of points in terms of their mutual distances," Psychometrika, Springer;The Psychometric Society, vol. 3(1), pages 19-22, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Si-Tong Lu & Miao Zhang & Qing-Na Li, 2020. "Feasibility and a fast algorithm for Euclidean distance matrix optimization with ordinal constraints," Computational Optimization and Applications, Springer, vol. 76(2), pages 535-569, June.
    2. J. Carroll, 1985. "Review," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 133-140, March.
    3. Aurea Grané & Rosario Romera, 2018. "On Visualizing Mixed-Type Data," Sociological Methods & Research, , vol. 47(2), pages 207-239, March.
    4. Jacqueline Meulman, 1992. "The integration of multidimensional scaling and multivariate analysis with optimal transformations," Psychometrika, Springer;The Psychometric Society, vol. 57(4), pages 539-565, December.
    5. Michael W. Trosset, 2002. "Extensions of Classical Multidimensional Scaling via Variable Reduction," Computational Statistics, Springer, vol. 17(2), pages 147-163, July.
    6. Beniaich, Adnane & Guimarães, Danielle Vieira & Avanzi, Junior Cesar & Silva, Bruno Montoani & Acuña-Guzman, Salvador Francisco & dos Santos, Wharley Pereira & Silva, Marx Leandro Naves, 2023. "Spontaneous vegetation as an alternative to cover crops in olive orchards reduces water erosion and improves soil physical properties under tropical conditions," Agricultural Water Management, Elsevier, vol. 279(C).
    7. Giuseppe Arbia & Giovanni Lafratta, 2002. "Anisotropic spatial sampling designs for urban pollution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(2), pages 223-234, May.
    8. Samuel Shye, 2010. "The Motivation to Volunteer: A Systemic Quality of Life Theory," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 98(2), pages 183-200, September.
    9. Muñoz-Mas, Rafael & Vezza, Paolo & Alcaraz-Hernández, Juan Diego & Martínez-Capel, Francisco, 2016. "Risk of invasion predicted with support vector machines: A case study on northern pike (Esox Lucius, L.) and bleak (Alburnus alburnus, L.)," Ecological Modelling, Elsevier, vol. 342(C), pages 123-134.
    10. Liwei Zhang & Shengzhe Gao & Saoyan Guo, 2019. "Statistical Inference of Second-Order Cone Programming," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(02), pages 1-17, April.
    11. Simensen, Trond & Halvorsen, Rune & Erikstad, Lars, 2018. "Methods for landscape characterisation and mapping: A systematic review," Land Use Policy, Elsevier, vol. 75(C), pages 557-569.
    12. Silvia Vilčeková & Ilija Zoran Apostoloski & Ľudmila Mečiarová & Eva Krídlová Burdová & Jozef Kiseľák, 2017. "Investigation of Indoor Air Quality in Houses of Macedonia," IJERPH, MDPI, vol. 14(1), pages 1-12, January.
    13. Funk, Patrick & Davis, Alex & Vaishnav, Parth & Dewitt, Barry & Fuchs, Erica, 2020. "Individual inconsistency and aggregate rationality: Overcoming inconsistencies in expert judgment at the technical frontier," Technological Forecasting and Social Change, Elsevier, vol. 155(C).
    14. Kuroda, Kaori & Hashiguchi, Hiroki & Fujiwara, Kantaro & Ikeguchi, Tohru, 2014. "Reconstruction of network structures from marked point processes using multi-dimensional scaling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 194-204.
    15. Fengzhen Zhai & Qingna Li, 2020. "A Euclidean distance matrix model for protein molecular conformation," Journal of Global Optimization, Springer, vol. 76(4), pages 709-728, April.
    16. Moris Triventi, 2014. "Higher education regimes: an empirical classification of higher education systems and its relationship with student accessibility," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(3), pages 1685-1703, May.
    17. Jessica Dafflon & Pedro F. Da Costa & František Váša & Ricardo Pio Monti & Danilo Bzdok & Peter J. Hellyer & Federico Turkheimer & Jonathan Smallwood & Emily Jones & Robert Leech, 2022. "A guided multiverse study of neuroimaging analyses," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    18. Karim Abou-Moustafa & Frank P. Ferrie, 2018. "Local generalized quadratic distance metrics: application to the k-nearest neighbors classifier," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(2), pages 341-363, June.
    19. Camacho, Maximo & Perez-Quiros, Gabriel & Saiz, Lorena, 2006. "Are European business cycles close enough to be just one?," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1687-1706.
    20. Shun Arahata & Takayuki Okuno & Akiko Takeda, 2023. "Complexity analysis of interior-point methods for second-order stationary points of nonlinear semidefinite optimization problems," Computational Optimization and Applications, Springer, vol. 86(2), pages 555-598, November.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:87:y:2023:i:2:d:10.1007_s10898-022-01188-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.