IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v153y2012i2d10.1007_s10957-011-9961-9.html
   My bibliography  Save this article

Necessary Optimality Conditions and New Optimization Methods for Cubic Polynomial Optimization Problems with Mixed Variables

Author

Listed:
  • Z. Y. Wu

    (University of Ballarat)

  • J. Quan

    (Yibin University)

  • G. Q. Li

    (Shanghai University)

  • J. Tian

    (University of Ballarat)

Abstract

Multivariate cubic polynomial optimization problems, as a special case of the general polynomial optimization, have a lot of practical applications in real world. In this paper, some necessary local optimality conditions and some necessary global optimality conditions for cubic polynomial optimization problems with mixed variables are established. Then some local optimization methods, including weakly local optimization methods for general problems with mixed variables and strongly local optimization methods for cubic polynomial optimization problems with mixed variables, are proposed by exploiting these necessary local optimality conditions and necessary global optimality conditions. A global optimization method is proposed for cubic polynomial optimization problems by combining these local optimization methods together with some auxiliary functions. Some numerical examples are also given to illustrate that these approaches are very efficient.

Suggested Citation

  • Z. Y. Wu & J. Quan & G. Q. Li & J. Tian, 2012. "Necessary Optimality Conditions and New Optimization Methods for Cubic Polynomial Optimization Problems with Mixed Variables," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 408-435, May.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:2:d:10.1007_s10957-011-9961-9
    DOI: 10.1007/s10957-011-9961-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-011-9961-9
    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/s10957-011-9961-9?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. Yanjun Wang & Zhian Liang, 2010. "Global optimality conditions for cubic minimization problem with box or binary constraints," Journal of Global Optimization, Springer, vol. 47(4), pages 583-595, August.
    2. Hanoch, Giora & Levy, Haim, 1970. "Efficient Portfolio Selection with Quadratic and Cubic Utility," The Journal of Business, University of Chicago Press, vol. 43(2), pages 181-189, April.
    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. Z. Wu & J. Tian & J. Ugon, 2015. "Global optimality conditions and optimization methods for polynomial programming problems," Journal of Global Optimization, Springer, vol. 62(4), pages 617-641, August.
    2. Wu, Zhiyou & Tian, Jing & Quan, Jing & Ugon, Julien, 2014. "Optimality conditions and optimization methods for quartic polynomial optimization," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 968-982.

    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. Sugu M.M. Zuhair & Daniel B. Taylor & Randall A. Kramer, 1992. "Choice of utility function form: its effect on classification of risk preferences and the prediction of farmer decisions," Agricultural Economics, International Association of Agricultural Economists, vol. 6(4), pages 333-344, April.
    2. Flores-Ortega, Miguel. & Flores-Castillo, Lilia Alejandra. & Paredes-Gómez, Angelica., 2014. "Selección de portafolios de inversión incluyendo el efecto de asimetría: evidencia con activos de la Bolsa Mexicana de Valores," Panorama Económico, Escuela Superior de Economía, Instituto Politécnico Nacional, vol. 0(19), pages 77-101, segundo s.
    3. Gourieroux, C. & Monfort, A., 2005. "The econometrics of efficient portfolios," Journal of Empirical Finance, Elsevier, vol. 12(1), pages 1-41, January.
    4. Xue-Gang Zhou & Xiao-Peng Yang & Bing-Yuan Cao, 2015. "Global optimality conditions for cubic minimization problems with cubic constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(3), pages 243-264, December.
    5. Drynan, Ross G., 1986. "A Note On Optimal Rules For Stochastic Efficiency Analysis," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 30(1), pages 1-10, April.
    6. Moshe Leshno & Haim Levy, 2002. "Preferred by "All" and Preferred by "Most" Decision Makers: Almost Stochastic Dominance," Management Science, INFORMS, vol. 48(8), pages 1074-1085, August.
    7. Chunhachinda, Pornchai & Dandapani, Krishnan & Hamid, Shahid & Prakash, Arun J., 1997. "Portfolio selection and skewness: Evidence from international stock markets," Journal of Banking & Finance, Elsevier, vol. 21(2), pages 143-167, February.
    8. Eric Jondeau & Michael Rockinger, 2006. "Optimal Portfolio Allocation under Higher Moments," European Financial Management, European Financial Management Association, vol. 12(1), pages 29-55, January.
    9. Hollstein, Fabian & Nguyen, Duc Binh Benno & Prokopczuk, Marcel, 2019. "Asset prices and “the devil(s) you know”," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 20-35.
    10. Post, Thierry & van Vliet, Pim, 2006. "Downside risk and asset pricing," Journal of Banking & Finance, Elsevier, vol. 30(3), pages 823-849, March.
    11. Simaan, Yusif, 2014. "The opportunity cost of mean–variance choice under estimation risk," European Journal of Operational Research, Elsevier, vol. 234(2), pages 382-391.
    12. Ramaratnam, S. Sri & Rister, M. Edward & Bessler, David A. & Novak, James, 1986. "Risk Attitudes and Farm/Producer Attributes: A Case Study of Texas Coastal Bend Grain Sorghum Producers," Journal of Agricultural and Applied Economics, Cambridge University Press, vol. 18(2), pages 85-96, December.
    13. George Samartzis & Nikitas Pittis, 2022. "On The Equivalence Of The Mean Variance Criterion And Stochastic Dominance Criteria," Papers 2211.01240, arXiv.org.
    14. Hardaker, J. Brian & Tanago, A.G., 1973. "Assessment Of The Output Of A Stochastic Decision Model," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 17(3), pages 1-9, December.
    15. Chunling Luo & Chin Hon Tan, 2020. "Almost Stochastic Dominance for Most Risk-Averse Decision Makers," Decision Analysis, INFORMS, vol. 17(2), pages 169-184, June.
    16. Post, G.T., 2003. "Asset prices and omitted moments; A stochastic dominance analysis of market efficiency," ERIM Report Series Research in Management ERS-2003-017-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    17. V. Jeyakumar & G. Li & S. Srisatkunarajah, 2014. "Global optimality principles for polynomial optimization over box or bivalent constraints by separable polynomial approximations," Journal of Global Optimization, Springer, vol. 58(1), pages 31-50, January.
    18. Eric Luxenberg & Stephen Boyd, 2022. "Portfolio Construction with Gaussian Mixture Returns and Exponential Utility via Convex Optimization," Papers 2205.04563, arXiv.org, revised Aug 2022.
    19. Drynan, Ross G., 1987. "Sufficient Conditions for Dominance of Simply Related Prospects," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 55(01), pages 1-12, April.
    20. Leonardo Lozano & David Bergman & J. Cole Smith, 2020. "On the Consistent Path Problem," Operations Research, INFORMS, vol. 68(6), pages 1913-1931, November.

    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:153:y:2012:i:2:d:10.1007_s10957-011-9961-9. 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.