Optimality conditions and duality results for non-differentiable interval optimization problems

Generalized-Hukuhara Subgradient and its Application in Optimization Problem with Interval-valued Functions

“…Apart from these, based on parametric representations of the IVFs, some authors [5,12,14] studied IOPs and developed theories to obtain the solutions to IOPs by converting them into real-valued optimization problems. The authors of [6] proposed some optimality conditions and duality results of a nonsmooth convex IOP using the parametric representation of its interval-valued objective and constrained functions. However, the parametric process is also practically difficult.…”

Generalized Hukuhara-Clarke Derivative of Interval-valued Functions and its Properties

“…Most often [4,14,32,37], IOPs have been analyzed with respect to a partial ordering [20]. Some researchers [3,11] used ordering relations of intervals based on the parametric comparison of intervals. In [7], an ordering relation of intervals is defined by a bijective correspondence between intervals and the points in R 2 .…”

“…In [7], an ordering relation of intervals is defined by a bijective correspondence between intervals and the points in R 2 . However, these ordering relations [3,11,7] of intervals can be derived from the relations described in [20]. Sengupta et al [30] proposed an acceptability function for intervals, just like a fuzzy membership function.…”

Optimality Conditions of Interval-Valued Optimization Problems by Using Subdifferantials

“…Hernández and Rodríguez-Marín [10], Karaman et al [11] Chen and Jahn [12] obtained some results for set optimization and vector optimization by using subdifferential, respectively. Wu [13] and Bhurjee and Padhan [14] obtained some optimality conditions for interval optimization by using duality. Also, Wu [15] and Chalco-Cano et al [16] used derivative to obtain solution for interval optimization.…”