IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v164y2015i1d10.1007_s10957-014-0530-x.html
   My bibliography  Save this article

Boundedness of a Type of Iterative Sequences in Two-Dimensional Quadratic Programming

Author

Listed:
  • Hoang Ngoc Tuan

    (Hanoi Pedagogical University)

Abstract

We prove that any iterative sequence generated by the projection decomposition algorithm of Pham Dinh et al. (Optim Methods Softw 23:609–629, 2008) in quadratic programming is bounded, provided that the quadratic program in question is two-dimensional and solvable.

Suggested Citation

  • Hoang Ngoc Tuan, 2015. "Boundedness of a Type of Iterative Sequences in Two-Dimensional Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 234-245, January.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:1:d:10.1007_s10957-014-0530-x
    DOI: 10.1007/s10957-014-0530-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-014-0530-x
    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/s10957-014-0530-x?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. Hoai Le Thi & Tao Pham Dinh & Nguyen Yen, 2012. "Behavior of DCA sequences for solving the trust-region subproblem," Journal of Global Optimization, Springer, vol. 53(2), pages 317-329, June.
    2. Hoai Le Thi & Tao Pham Dinh & Nguyen Yen, 2011. "Properties of two DC algorithms in quadratic programming," Journal of Global Optimization, Springer, vol. 49(3), pages 481-495, March.
    3. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    4. Hoang Ngoc Tuan, 2012. "Convergence Rate of the Pham Dinh–Le Thi Algorithm for the Trust-Region Subproblem," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 904-915, September.
    5. G. M. Lee & N. N. Tam & N. D. Yen, 2006. "Continuity of the Solution Map in Quadratic Programs under Linear Perturbations," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 415-423, June.
    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. Hoai An Le Thi & Van Ngai Huynh & Tao Pham Dinh, 2018. "Convergence Analysis of Difference-of-Convex Algorithm with Subanalytic Data," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 103-126, October.
    2. Nguyen Thanh Qui, 2016. "Coderivatives of implicit multifunctions and stability of variational systems," Journal of Global Optimization, Springer, vol. 65(3), pages 615-635, July.
    3. Karan N. Chadha & Ankur A. Kulkarni, 2022. "On independent cliques and linear complementarity problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(4), pages 1036-1057, December.
    4. 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.
    5. Zhang, Yongxiong & Zheng, Hua & Lu, Xiaoping & Vong, Seakweng, 2023. "Modulus-based synchronous multisplitting iteration methods without auxiliary variable for solving vertical linear complementarity problems," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    6. Guo-qiang Wang & Yu-jing Yue & Xin-zhong Cai, 2009. "Weighted-path-following interior-point algorithm to monotone mixed linear complementarity problem," Fuzzy Information and Engineering, Springer, vol. 1(4), pages 435-445, December.
    7. van der Laan, Gerard & Talman, Dolf & Yang, Zaifu, 2011. "Solving discrete systems of nonlinear equations," European Journal of Operational Research, Elsevier, vol. 214(3), pages 493-500, November.
    8. Zheng-Hai Huang & Yu-Fan Li & Yong Wang, 2023. "A fixed point iterative method for tensor complementarity problems with the implicit Z-tensors," Journal of Global Optimization, Springer, vol. 86(2), pages 495-520, June.
    9. Christoph Böhringer & Thomas F. Rutherford, 2017. "Paris after Trump: An Inconvenient Insight," CESifo Working Paper Series 6531, CESifo.
    10. G. L. Zhou & L. Caccetta, 2008. "Feasible Semismooth Newton Method for a Class of Stochastic Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 379-392, November.
    11. Nguyen Qui, 2014. "Stability for trust-region methods via generalized differentiation," Journal of Global Optimization, Springer, vol. 59(1), pages 139-164, May.
    12. A. K. Das, 2016. "Properties of some matrix classes based on principal pivot transform," Annals of Operations Research, Springer, vol. 243(1), pages 375-382, August.
    13. Meijuan Shang & Chao Zhang & Naihua Xiu, 2014. "Minimal Zero Norm Solutions of Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 795-814, December.
    14. Massol, Olivier & Rifaat, Omer, 2018. "Phasing out the U.S. Federal Helium Reserve: Policy insights from a world helium model," Resource and Energy Economics, Elsevier, vol. 54(C), pages 186-211.
    15. S. R. Mohan, 1997. "Degeneracy Subgraph of the Lemke Complementary Pivot Algorithm and Anticycling Rule," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 409-423, August.
    16. Thiruvankatachari Parthasarathy & Gomatam Ravindran & Sunil Kumar, 2022. "On Semimonotone Matrices, $$R_0$$ R 0 -Matrices and Q-Matrices," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 131-147, October.
    17. Y. P. Fang & N. J. Huang, 2006. "Feasibility and Solvability for Vector Complementarity Problems1," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 373-390, June.
    18. Xiaojun Chen & Yun Shi & Xiaozhou Wang, 2020. "Equilibrium Oil Market Share under the COVID-19 Pandemic," Papers 2007.15265, arXiv.org.
    19. Dongmei Yu & Huiling Wei & Cairong Chen & Deren Han, 2024. "Scalable Relaxation Two-Sweep Modulus-Based Matrix Splitting Methods for Vertical LCP," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 714-744, October.
    20. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2005. "Computing Integral Solutions of Complementarity Problems," Other publications TiSEM b8e0c74e-2219-4ab0-99a2-0, Tilburg University, School of Economics and Management.

    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:joptap:v:164:y:2015:i:1:d:10.1007_s10957-014-0530-x. 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.