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Efficient Solutions of Interval Programming Problems with Inexact Parameters and Second Order Cone Constraints

Author

Listed:
  • Ali Sadeghi

    (Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, 6135743136 Ahavaz, Iran)

  • Mansour Saraj

    (Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, 6135743136 Ahavaz, Iran)

  • Nezam Mahdavi Amiri

    (Faculty of Mathematical Sciences, Sharif University of Technology, 11365-11155 Tehran, Iran)

Abstract

In this article, a methodology is developed to solve an interval and a fractional interval programming problem by converting into a non-interval form for second order cone constraints, with the objective function and constraints being interval valued functions. We investigate the parametric and non-parametric forms of the interval valued functions along with their convexity properties. Two approaches are developed to obtain efficient and properly efficient solutions. Furthermore, the efficient solutions or Pareto optimal solutions of fractional and non-fractional programming problems over R + n ⋃ { 0 } are also discussed. The main idea of the present article is to introduce a new concept for efficiency, called efficient space, caused by the lower and upper bounds of the respective intervals of the objective function which are shown in different figures. Finally, some numerical examples are worked through to illustrate the methodology and affirm the validity of the obtained results.

Suggested Citation

  • Ali Sadeghi & Mansour Saraj & Nezam Mahdavi Amiri, 2018. "Efficient Solutions of Interval Programming Problems with Inexact Parameters and Second Order Cone Constraints," Mathematics, MDPI, vol. 6(11), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:11:p:270-:d:184269
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    References listed on IDEAS

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    1. Yu. E. Nesterov & M. J. Todd, 1997. "Self-Scaled Barriers and Interior-Point Methods for Convex Programming," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 1-42, February.
    2. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
    3. A. Bhurjee & G. Panda, 2012. "Efficient solution of interval optimization problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 273-288, December.
    4. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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