Advanced Search
Article Contents
Article Contents

Saddle-point type optimality criteria, duality and a new approach for solving nonsmooth fractional continuous-time programming problems

This research was supported by the Science Fund of the Republic of Serbia, Grant No. 7744592, Integrability and Extremal Problems in Mechanics, Geometry and Combinatorics-MEGIC

Abstract / Introduction Full Text(HTML) Related Papers Cited by
  • In this paper, fractional continuous-time programming problems with inequality phase constraints are considered. Optimality conditions and duality results under a certain regularity condition are derived. All functions are assumed to be nondifferentiable. These results improve and generalize a number of existing results in the area of fractional continuous-time programming. We provide a practical example to illustrate our results.

    Mathematics Subject Classification: Primary: 90C30; 90C32; 90C46.


    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] A. V. ArutunovS. E. Zhukovskiy and B. Marinkovic, Theorems of the alternative for systems of convex inequalities, Set-Valued and Variational Analysis, 27 (2019), 51-70.  doi: 10.1007/s11228-017-0406-y.
    [2] R. Bellman, Bottleneck problems and dynamic programming, Proc. Natl. Acad. Sci., 39 (1953), 947-951.  doi: 10.1073/pnas.39.9.947.
    [3] A. J. V. BrandaoM. A. Rojas-Medar and G. N. Silva, Nonsmooth continuous-time optimization problems: Necessary conditions, Comput. Math. Appl., 41 (2001), 1477-1486.  doi: 10.1016/S0898-1221(01)00112-2.
    [4] B. D. Craven, Mathematical Programming and Control Theory, Chapman Hall, London, 1978.
    [5] B. D. Craven, Fractional Programming, Heldermann Verlag, Berlin, 1988.
    [6] G. Gol'stein, Theory of Convex Programming, Trans. Math. Mono. Amer. Math. Soc., Providence, RI., 1972.
    [7] S. Nobakhtian and M. Pouryayevali, Optimality conditions and duality for nonsmooth fractional continuous-time problems, Journal of Optimization Theory and Applications, 152 (2012), 245-255.  doi: 10.1007/s10957-010-9693-2.
    [8] S. Schaible, Bibliography in fractional programming, Zeitschrift fur Operations Research, 26 (1982), 211-241.  doi: 10.1007/bf01917115.
    [9] A. M. Stancu, Mathematical Programming with Type-I Functions, Matrix Rom., Bucharest, 2013.
    [10] A. M. Stancu and I. M. Stancu-Minasian, Sufficiency criteria in continuous-time nonlinear programming under generalized ($\alpha$, $\rho$)-($\eta$, $\theta$) - type Ⅰ invexity, Rev. Roumaine Math. Pures Appl., 56 (2011), 169-179. 
    [11] A. M. Stancu and I. M. Stancu-Minasian, Carathéodory-John-type sufficiency criteria in continuous-time nonlinear programming under generalized ($\alpha$, $\rho$)-($\eta$, $\theta$) - type Ⅰ invexity, Math. Reports, 16 (2012), 345-354. 
    [12] I. M. Stancu-Minasian, Fractional Programming. Theory, Methods and Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997. doi: 10.1007/978-94-009-0035-6.
    [13] I. M. Stancu-Minasian, An eighth bibliography of fractional programming, Optimization, 66 (2017), 439-470.  doi: 10.1080/02331934.2016.1276179.
    [14] I. M. Stancu-Minasian, A ninth bibliography of fractional programming. With supplemental material "A classification due to the bibliography on fractional programming" by I. M. Stancu-Minasian, Optimization, 68 (2019), 2125-2169.  doi: 10.1080/02331934.2019.1632250.
    [15] I. M. Stancu-Minasian and S. Tigan, Continuous time linear-fractional programming. The minimum-risk approach, RAIRO-Oper.Res., 34 (2000), 397-409.  doi: 10.1051/ro:2000121.
    [16] C. Wen and H. Wu, Using the Dinkelbach-type algorithm to solve the continuous-time linear fractional Programming Problems, Journal of Global Optimization, 49 (2011), 237-263.  doi: 10.1007/s10898-010-9542-8.
    [17] C. Wen and H. Wu, Approximate solutions and duality theorems for continuous-time linear fractional programming problems, Numerical Functional Analysis and Optimization, 33 (2012), 80-129.  doi: 10.1080/01630563.2011.629312.
    [18] C. Wen and H. Wu, Using the parametric approach to solve the continuous-time linear fractional max-min problems, Journal of Global Optimization, 54 (2012), 129-153.  doi: 10.1007/s10898-011-9751-9.
    [19] G. J. Zalmai, A continuous time generalization of Gordan's transposition theorem, J. Math. Anal. Appl., 110 (1985), 130-140.  doi: 10.1016/0022-247X(85)90339-7.
    [20] G. J. Zalmai, The Fritz John and Kuhn-Tucker optimality conditions in continuous-time programming, J. Math. Anal. Appl., 110 (1985), 503-518.  doi: 10.1016/0022-247X(85)90312-9.
    [21] G. J. Zalmai, Duality for a class of continuous-time homogeneous fractional programming problems, Z. Oper. Res., Ser. A-B 30 (1986), 43-48.  doi: 10.1007/BF01918630.
    [22] G. J. Zalmai, Optimality conditions and duality models for a class of nonsmooth continuous-time fractional programming problems, J. Stat. Manag. Sy. St., 1 (1998), 141-173.  doi: 10.1080/09720510.1998.10700983.
  • 加载中

Article Metrics

HTML views(1436) PDF downloads(381) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint