Generalized Hukuhara Global Subdifferentiability in Interval Optimization Problems

Krishan Kumar () and Debdas Ghosh ()
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Krishan Kumar: Indian Institute of Technology (Banaras Hindu University) Varanasi, Department of Mathematical Sciences
Debdas Ghosh: Indian Institute of Technology (Banaras Hindu University) Varanasi, Department of Mathematical Sciences

Chapter Chapter 7 in Fuzzy Optimization, Decision-making and Operations Research, 2023, pp 135-160 from Springer

Abstract: Abstract In this chapter, we propose the concept of generalized Hukuhara (gH)-global subdifferential for interval-valued function (IVF). To define this concept, we propose the notions of gH-lower and gH-upper global directional derivatives for IVFs. A few results on the characteristics of gH-lower and gH-upper global subdifferential are studied. Next, a result on the gH-directional derivative of the maximum of comparable IVFs is derived. In the sequel, a comparison of gH-lower subdifferential is given with gH-Fréchet subdifferential, gH-proximal subdifferential, and gH-subdifferential for IVFs. Thereafter, a necessary and sufficient condition for obtaining an efficient solution to an interval optimization problem (IOP) with the help of gH-lower global subdifferential is given.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-35668-1_7

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DOI: 10.1007/978-3-031-35668-1_7

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