IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v162y2014i1d10.1007_s10957-013-0417-2.html
   My bibliography  Save this article

On the Indefinite Quadratic Fractional Optimization with Two Quadratic Constraints

Author

Listed:
  • S. Fallahi

    (University of Guilan)

  • M. Salahi

    (University of Guilan)

Abstract

In this paper, we consider minimizing the ratio of two indefinite quadratic functions subject to two quadratic constraints. Using the extension of Charnes–Cooper transformation, we transform the problem to a homogenized quadratic problem. Then, we show that, under certain assumptions, it can be solved to global optimality using semidefinite optimization relaxation.

Suggested Citation

  • S. Fallahi & M. Salahi, 2014. "On the Indefinite Quadratic Fractional Optimization with Two Quadratic Constraints," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 249-256, July.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:1:d:10.1007_s10957-013-0417-2
    DOI: 10.1007/s10957-013-0417-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-013-0417-2
    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/s10957-013-0417-2?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Lo, Andrew W. & Mackinlay, A. Craig, 1997. "Maximizing Predictability In The Stock And Bond Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 1(1), pages 102-134, January.
    2. Jos F. Sturm & Shuzhong Zhang, 2003. "On Cones of Nonnegative Quadratic Functions," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 246-267, May.
    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. Van-Bong Nguyen & Thi Ngan Nguyen & Ruey-Lin Sheu, 2020. "Strong duality in minimizing a quadratic form subject to two homogeneous quadratic inequalities over the unit sphere," Journal of Global Optimization, Springer, vol. 76(1), pages 121-135, January.

    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. Shinji Yamada & Akiko Takeda, 2018. "Successive Lagrangian relaxation algorithm for nonconvex quadratic optimization," Journal of Global Optimization, Springer, vol. 71(2), pages 313-339, June.
    2. Bruno Breyer Caldas & João Frois Caldeira & Guilherme Vale Moura, 2016. "Is Pairs Trading Performance Sensitive To The Methodologies?: A Comparison," Anais do XLII Encontro Nacional de Economia [Proceedings of the 42nd Brazilian Economics Meeting] 130, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    3. Ben-Tal, A. & den Hertog, D., 2011. "Immunizing Conic Quadratic Optimization Problems Against Implementation Errors," Discussion Paper 2011-060, Tilburg University, Center for Economic Research.
    4. Andrew W. Lo & Harry Mamaysky & Jiang Wang, 2000. "Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation," Journal of Finance, American Finance Association, vol. 55(4), pages 1705-1765, August.
    5. Wen-Jun Xue & Li-Wen Zhang, 2016. "Stock Return Autocorrelations and Predictability in the Chinese Stock Market: Evidence from Threshold Quantile Autoregressive Models," Working Papers 1605, Florida International University, Department of Economics.
    6. Cheung, Yin-Wong & He, Jia & Ng, Lilian K., 1997. "What are the global sources of rational variation in international equity returns?," Journal of International Money and Finance, Elsevier, vol. 16(6), pages 821-836, December.
    7. Xinzhen Zhang & Chen Ling & Liqun Qi, 2011. "Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints," Journal of Global Optimization, Springer, vol. 49(2), pages 293-311, February.
    8. Bomze, Immanuel M. & Gabl, Markus, 2023. "Optimization under uncertainty and risk: Quadratic and copositive approaches," European Journal of Operational Research, Elsevier, vol. 310(2), pages 449-476.
    9. Nuerxiati Abudurexiti & Kai He & Dongdong Hu & Svetlozar T. Rachev & Hasanjan Sayit & Ruoyu Sun, 2021. "Portfolio analysis with mean-CVaR and mean-CVaR-skewness criteria based on mean-variance mixture models," Papers 2111.04311, arXiv.org, revised Feb 2023.
    10. Meghana Ayyagari & Asli Demirgüç-Kunt & Vojislav Maksimovic, 2013. "What Determines Protection of Property Rights? An Analysis of Direct and Indirect Effects," Journal of Financial Econometrics, Oxford University Press, vol. 11(4), pages 610-649, September.
    11. R. Yamamoto & H. Konno, 2007. "An Efficient Algorithm for Solving Convex–Convex Quadratic Fractional Programs," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 241-255, May.
    12. Frenk, J.B.G. & Schaible, S., 2004. "Fractional Programming," Econometric Institute Research Papers ERS-2004-074-LIS, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    13. Immanuel Bomze & Werner Schachinger & Gabriele Uchida, 2012. "Think co(mpletely)positive ! Matrix properties, examples and a clustered bibliography on copositive optimization," Journal of Global Optimization, Springer, vol. 52(3), pages 423-445, March.
    14. Cheng Lu & Zhibin Deng & Jing Zhou & Xiaoling Guo, 2019. "A sensitive-eigenvector based global algorithm for quadratically constrained quadratic programming," Journal of Global Optimization, Springer, vol. 73(2), pages 371-388, February.
    15. Andrew W. Lo & Jiang Wang, 2006. "Trading Volume: Implications of an Intertemporal Capital Asset Pricing Model," Journal of Finance, American Finance Association, vol. 61(6), pages 2805-2840, December.
    16. Philippe Goulet Coulombe & Maximilian Goebel, 2023. "Maximally Machine-Learnable Portfolios," Papers 2306.05568, arXiv.org, revised Apr 2024.
    17. Yochanan Shachmurove & Uri BenZion & Paul Klein & Joseph Yagil, 2001. "A Moving Average Comparison of the Tel-Aviv 25 and S&P 500 Stock Indices," Penn CARESS Working Papers 4731f3394c43bebf4d3191c81, Penn Economics Department.
    18. Jing Zhou & Shu-Cherng Fang & Wenxun Xing, 2017. "Conic approximation to quadratic optimization with linear complementarity constraints," Computational Optimization and Applications, Springer, vol. 66(1), pages 97-122, January.
    19. Xue, Wen-Jun & Zhang, Li-Wen, 2017. "Stock return autocorrelations and predictability in the Chinese stock market—Evidence from threshold quantile autoregressive models," Economic Modelling, Elsevier, vol. 60(C), pages 391-401.
    20. Harold P. Benson, 2006. "Maximizing the ratio of two convex functions over a convex set," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(4), pages 309-317, June.

    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:162:y:2014:i:1:d:10.1007_s10957-013-0417-2. 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.