IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v129y2006i3d10.1007_s10957-006-9076-x.html
   My bibliography  Save this article

Continuity of the Solution Map in Quadratic Programs under Linear Perturbations

Author

Listed:
  • G. M. Lee

    (Pukyong National University)

  • N. N. Tam

    (Hanoi Pedagogical Institute No. 2)

  • N. D. Yen

    (Vietnamese Academy of Science and Technology)

Abstract

It is well known that the solution map of a quadratic program where only the linear part of the data is subject to perturbation is an upper Lipschitz multifunction. This paper characterizes the continuity and lower semicontinuity of that solution map.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:129:y:2006:i:3:d:10.1007_s10957-006-9076-x
    DOI: 10.1007/s10957-006-9076-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-006-9076-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/s10957-006-9076-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. E. Blum & W. Oettli, 1972. "Technical Note—Direct Proof of the Existence Theorem for Quadratic Programming," Operations Research, INFORMS, vol. 20(1), pages 165-167, February.
    2. 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.
    3. B. Curtis Eaves, 1971. "On Quadratic Programming," Management Science, INFORMS, vol. 17(11), pages 698-711, July.
    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. 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.
    2. Hoang Phu & Vo Pho, 2010. "Global infimum of strictly convex quadratic functions with bounded perturbations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 327-345, October.
    3. H. X. Phu & V. M. Pho & P. T. An, 2011. "Maximizing Strictly Convex Quadratic Functions with Bounded Perturbations," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 1-25, April.

    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. 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.
    2. 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.
    3. 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.
    4. Musshoff, Oliver & Hirschauer, Norbert, 2004. "Optimierung unter Unsicherheit mit Hilfe stochastischer Simulation und Genetischer Algorithmen – dargestellt anhand der Optimierung des Produktionsprogramms eines Brandenburger Marktfruchtbetriebes," German Journal of Agricultural Economics, Humboldt-Universitaet zu Berlin, Department for Agricultural Economics, vol. 53(07), pages 1-16.
    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. Erasmus, Barend & van Jaarsveld, Albert & van Zyl, Johan & Vink, Nick, 2000. "The effects of climate change on the farm sector in the Western Cape," Agrekon, Agricultural Economics Association of South Africa (AEASA), vol. 39(4), pages 1-15, December.
    9. Luo, Z-Q. & Zhang, S., 1997. "On the extensions of the Frank-Worfe theorem," Econometric Institute Research Papers EI 9748/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    10. 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.
    11. Christoph Böhringer & Thomas F. Rutherford, 2017. "Paris after Trump: An Inconvenient Insight," CESifo Working Paper Series 6531, CESifo.
    12. Louhichi, Kamel & Flichman, Guillermo & Blanco Fonseca, Maria, 2009. "A generic template for FSSIM," Reports 57463, Wageningen University, SEAMLESS: System for Environmental and Agricultural Modelling; Linking European Science and Society.
    13. 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.
    14. 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.
    15. Paudel, K. P. & Lohr, L. & Martin, N. R., 2000. "Effect of risk perspective on fertilizer choice by sharecroppers," Agricultural Systems, Elsevier, vol. 66(2), pages 115-128, November.
    16. 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.
    17. 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.
    18. 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.
    19. Norton, George W., 1976. "Constraints To Increasing Livestock Production In Less Developed Countries: A Literature Review," Staff Papers 14043, University of Minnesota, Department of Applied Economics.
    20. 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.

    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:129:y:2006:i:3:d:10.1007_s10957-006-9076-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.