Title: On optimality conditions for interval optimisation problems using generalised Hukuhara difference and constrained interval arithmetic
Authors: Shaveta Kumari; Saurabh Srivastava
Addresses: Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Solan, 173234, Himachal Pradesh, India ' Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Solan, 173234, Himachal Pradesh, India
Abstract: In the presented paper we derive necessary optimality conditions for mathematical optimisation problems which involve both objective function and inequality constraints in interval form. In the proposed work both objective function and inequality constraints are derived from continuous function. For the formation of continuous function we used the idea of generalised Hukuhara difference (gH-difference), generalised Hukuhara derivative and constrained interval arithmetic. The objective of this paper is to derive new necessary optimality conditions for interval valued optimisation problem on the basis of classical optimality conditions given by Karush-Kuhn-Tucker (KKT). Finally, the proposed conditions are illustrated with the help of numerical examples.
Keywords: generalised Hukuhara difference; generalised Hukuhara derivative; constrained interval arithmetic.
International Journal of Mathematics in Operational Research, 2021 Vol.19 No.2, pp.204 - 219
Received: 31 Aug 2019
Accepted: 28 Feb 2020
Published online: 20 Jul 2021 *