Advanced Search
Article Contents
Article Contents

Optimality and duality for complex multi-objective programming

  • * Corresponding author: Tone-Yau Huang

    * Corresponding author: Tone-Yau Huang 

The first author is supported by MOST 109-2115-M-035-002, Taiwan

Abstract Full Text(HTML) Figure(1) Related Papers Cited by
  • We consider a complex multi-objective programming problem (CMP). In order to establish the optimality conditions of problem (CMP), we introduce several properties of optimal efficient solutions and scalarization techniques. Furthermore, a certain parametric dual model is discussed, and their duality theorems are proved.

    Mathematics Subject Classification: Primary: 90C46, 90C29; Secondary: 49K35.


    \begin{equation} \\ \end{equation}
  • 加载中
  • Figure 1.  The graphs of Example 2.1

  • [1] R. A. Abrams, Nonlinear programming in complex space: sufficient conditions and duality, J. Math. Anal. Appl., 38 (1972), 619-632.  doi: 10.1016/0022-247X(72)90073-X.
    [2] R. A. Abrams and A. Ben-Israel, Complex mathematical programming, Developments in Operations Research (eds. B. Avi-Itzhak, Gordon and Breach), New York, (1971), 3–20.
    [3] R. A. Abrams and A. Ben-Israel, Nonlinear programming in complex space: necessary conditions, SIAM J. Control., 9 (1971), 606-620. 
    [4] N. Datta and D. Bhatia, Duality for a class of nondifferentiable mathematical programming problems in complex space, J. Math. Anal. Appl., 101 (1984), 1-11.  doi: 10.1016/0022-247X(84)90053-2.
    [5] D. I. Duca, On vectorial programming problem in complex space, Studia Univ. Babeș-Bolyai Math., 24 (1979), 51–56.
    [6] D. I. Duca, Proper efficiency in the complex vectorial programming, Studia Univ. Babeș-Bolyai Math., 25 (1980), 73–80.
    [7] D. I. Duca, Efficiency criteria in vectorial programming in complex space without convexity, Cahiers Centre Études Rech. Opér., 26 (1984), 217–226.
    [8] D. I. Duca, Multicriteria Optimization in Complex Space, Casa Cǎrţii de Ştiinţǎ, Cluj-Napoca, 2005.
    [9] M. E. Elbrolosy, Efficiency for a generalized form of vector optimization problems in complex space, Optimization, 65 (2016), 1245-1257.  doi: 10.1080/02331934.2015.1104680.
    [10] O. Ferrero, On nonlinear programming in complex spaces, J. Math. Anal. Appl., 164 (1992), 399-416.  doi: 10.1016/0022-247X(92)90123-U.
    [11] H. C. Lai and T. Y. Huang, Optimality conditions for a nondifferentiable minimax programming in complex spaces, Nonlinear Anal., 71 (2009), 1205-1212.  doi: 10.1016/j.na.2008.11.053.
    [12] H. C. Lai and T. Y. Huang, Optimality conditions for nondifferentiable minimax fractional programming with complex variables, J. Math. Anal. Appl., 359 (2009), 229-239.  doi: 10.1016/j.jmaa.2009.05.049.
    [13] H. C. Lai and T. Y. Huang, Nondifferentiable minimax fractional programming in complex spaces with parametric duality, J. Global Optim., 53 (2012), 243-254.  doi: 10.1007/s10898-011-9680-7.
    [14] H. C. Lai and T. Y. Huang, Mixed type duality for a nondifferentiable minimax fractional complex programming, Pacific J. Optim., 10 (2014), 305-319. 
    [15] H. C. Lai and J. C. Liu, Duality for nondifferentiable minimax programming in complex spaces, Nonlinear Anal., 71 (2009), e224–e233. doi: 10.1016/j.na.2008.10.062.
    [16] N. Levinson, Linear programming in complex space, J. Math. Anal. Appl., 14 (1966), 44-62.  doi: 10.1016/0022-247X(66)90061-8.
    [17] B. Mond and B. D. Craven, A class of nondifferentiable complex programming problems, J. Math. Oper. and Stat., 6 (1975), 581-591.  doi: 10.1007/bf01966096.
    [18] I. M. Stancu-MinasianD. I. Duca and T. Nishida, Multiple objective linear fractional optimization in complex space, Math. Japonica., 35 (1990), 195-203. 
    [19] Y. SawaragiH. Nakayama and  T. TaninoTheory of Multiobjective Optimization, Academic Press, Orlando, FL, 1985. 
    [20] E. A. Youness and M. E. Elbrolosy, Extension to necessary optimality conditions in complex programming, Appl. Math. Comput., 154 (2004), 229-237.  doi: 10.1016/S0096-3003(03)00706-9.
    [21] E. A. Youness and M. E. Elbrolosy, Extension to sufficient optimality conditions in complex programming, J. Math. Stat., 1 (2005), 40-48.  doi: 10.3844/jmssp.2005.40.48.
  • 加载中



Article Metrics

HTML views(182) PDF downloads(177) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint