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

Ali Sadeghi, Mansour Saraj and Nezam Mahdavi Amiri
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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

Mathematics, 2018, vol. 6, issue 11, 1-13

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.

Keywords: second order cone (SOC); interval programming; inexact parameter; efficient solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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