IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v22y2014i3p1148-1170.html
   My bibliography  Save this article

Concepts and techniques of optimization on the sphere

Author

Listed:
  • O. Ferreira
  • A. Iusem
  • S. Németh

Abstract

In this paper some concepts and techniques of Mathematical Programming are extended in an intrinsic way from the Euclidean space to the sphere. In particular, the notion of convex functions, variational problem and monotone vector fields are extended to the sphere and several characterizations of these notions are shown. As an application of the convexity concept, necessary and sufficient optimality conditions for constrained convex optimization problems on the sphere are derived. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • O. Ferreira & A. Iusem & S. Németh, 2014. "Concepts and techniques of optimization on the sphere," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 1148-1170, October.
    • Handle: RePEc:spr:topjnl:v:22:y:2014:i:3:p:1148-1170
    DOI: 10.1007/s11750-014-0322-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11750-014-0322-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11750-014-0322-3?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 search for a different version of it.

    References listed on IDEAS

    as
    1. O. P. Ferreira & P. R. Oliveira, 1998. "Subgradient Algorithm on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 97(1), pages 93-104, April.
    2. Akhlad Iqbal & Shahid Ali & I. Ahmad, 2012. "On Geodesic E-Convex Sets, Geodesic E-Convex Functions and E-Epigraphs," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 239-251, October.
    3. Laurent, M., 2009. "Sums of squares, moment matrices and optimization over polynomials," Other publications TiSEM 9fef820b-69d2-43f2-a501-e, Tilburg University, School of Economics and Management.
    4. O. Ferreira & A. Iusem & S. Németh, 2013. "Projections onto convex sets on the sphere," Journal of Global Optimization, Springer, vol. 57(3), pages 663-676, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fabiana R. de Oliveira & Orizon P. Ferreira, 2020. "Newton Method for Finding a Singularity of a Special Class of Locally Lipschitz Continuous Vector Fields on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 522-539, May.
    2. O. P. Ferreira & S. Z. Németh, 2019. "On the spherical convexity of quadratic functions," Journal of Global Optimization, Springer, vol. 73(3), pages 537-545, March.
    3. Henri Bonnel & Léonard Todjihoundé & Constantin Udrişte, 2015. "Semivectorial Bilevel Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 464-486, November.
    4. Peng Zhang & Gejun Bao, 2018. "An Incremental Subgradient Method on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 711-727, March.
    5. Orizon Pereira Ferreira & Sándor Zoltán Németh & Lianghai Xiao, 2020. "On the Spherical Quasi-convexity of Quadratic Functions on Spherically Subdual Convex Sets," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 1-21, October.
    6. Teles A. Fernandes & Orizon P. Ferreira & Jinyun Yuan, 2017. "On the Superlinear Convergence of Newton’s Method on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 828-843, June.

    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. O. P. Ferreira & S. Z. Németh, 2019. "On the spherical convexity of quadratic functions," Journal of Global Optimization, Springer, vol. 73(3), pages 537-545, March.
    2. Xiao Wang & Xinzhen Zhang & Guangming Zhou, 2020. "SDP relaxation algorithms for $$\mathbf {P}(\mathbf {P}_0)$$P(P0)-tensor detection," Computational Optimization and Applications, Springer, vol. 75(3), pages 739-752, April.
    3. João Carlos de O. Souza, 2018. "Proximal Point Methods for Lipschitz Functions on Hadamard Manifolds: Scalar and Vectorial Cases," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 745-760, December.
    4. Laurent, Monique & Vargas, Luis Felipe, 2022. "Finite convergence of sum-of-squares hierarchies for the stability number of a graph," Other publications TiSEM 3998b864-7504-4cf4-bc1d-f, Tilburg University, School of Economics and Management.
    5. Laurent, M. & Rostalski, P., 2012. "The approach of moments for polynomial equations," Other publications TiSEM f08f3cd2-b83e-4bf1-9322-a, Tilburg University, School of Economics and Management.
    6. Tomohiko Mizutani & Makoto Yamashita, 2013. "Correlative sparsity structures and semidefinite relaxations for concave cost transportation problems with change of variables," Journal of Global Optimization, Springer, vol. 56(3), pages 1073-1100, July.
    7. Fook Wai Kong & Polyxeni-Margarita Kleniati & Berç Rustem, 2012. "Computation of Correlated Equilibrium with Global-Optimal Expected Social Welfare," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 237-261, April.
    8. Sandra S. Y. Tan & Antonios Varvitsiotis & Vincent Y. F. Tan, 2021. "Analysis of Optimization Algorithms via Sum-of-Squares," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 56-81, July.
    9. J. X. Cruz Neto & F. M. O. Jacinto & P. A. Soares & J. C. O. Souza, 2018. "On maximal monotonicity of bifunctions on Hadamard manifolds," Journal of Global Optimization, Springer, vol. 72(3), pages 591-601, November.
    10. Hao Hu & Renata Sotirov, 2021. "The linearization problem of a binary quadratic problem and its applications," Annals of Operations Research, Springer, vol. 307(1), pages 229-249, December.
    11. Shenglong Hu & Guoyin Li & Liqun Qi, 2016. "A Tensor Analogy of Yuan’s Theorem of the Alternative and Polynomial Optimization with Sign structure," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 446-474, February.
    12. P. M. Kleniati & P. Parpas & B. Rustem, 2010. "Decomposition-based Method for Sparse Semidefinite Relaxations of Polynomial Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 289-310, May.
    13. X. M. Wang & C. Li & J. C. Yao, 2015. "Subgradient Projection Algorithms for Convex Feasibility on Riemannian Manifolds with Lower Bounded Curvatures," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 202-217, January.
    14. T. D. Chuong & V. Jeyakumar & G. Li, 2019. "A new bounded degree hierarchy with SOCP relaxations for global polynomial optimization and conic convex semi-algebraic programs," Journal of Global Optimization, Springer, vol. 75(4), pages 885-919, December.
    15. Papp, Dávid & Regős, Krisztina & Domokos, Gábor & Bozóki, Sándor, 2023. "The smallest mono-unstable convex polyhedron with point masses has 8 faces and 11 vertices," European Journal of Operational Research, Elsevier, vol. 310(2), pages 511-517.
    16. Jiawang Nie & Suhan Zhong, 2023. "Loss functions for finite sets," Computational Optimization and Applications, Springer, vol. 84(2), pages 421-447, March.
    17. Glaydston C. Bento & Jefferson G. Melo, 2012. "Subgradient Method for Convex Feasibility on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 773-785, March.
    18. Ruixue Zhao & Jinyan Fan, 2020. "Higher-degree tensor eigenvalue complementarity problems," Computational Optimization and Applications, Springer, vol. 75(3), pages 799-816, April.
    19. Guo-ji Tang & Nan-jing Huang, 2012. "Korpelevich’s method for variational inequality problems on Hadamard manifolds," Journal of Global Optimization, Springer, vol. 54(3), pages 493-509, November.
    20. Sönke Behrends & Anita Schöbel, 2020. "Generating Valid Linear Inequalities for Nonlinear Programs via Sums of Squares," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 911-935, September.

    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:topjnl:v:22:y:2014:i:3:p:1148-1170. 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.