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Efficient solutions of interval programming problems with inexact parameters and second order cone constraints. (English) Zbl 1404.90137
Summary: 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 \(\mathbb R_+^n \bigcup \{0 \}\) 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.
MSC:
90C46 Optimality conditions and duality in mathematical programming
90C29 Multi-objective and goal programming
Software:
SOCP
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