Abstract
In this paper, we present the gH-symmetrical derivative of interval-valued functions and its properties. In application, we apply this new derivative to investigate the Karush–Kuhn–Tucker (KKT) conditions of interval-valued optimization problems. Meanwhile, some examples are worked out to illuminate the obtained results.
Highlights
In modern times, the optimization problems with uncertainty have received considerable attention and have great value in economic and control fields (e.g., [1,2,3,4])
We defined the gH-symmetrical derivative of interval-valued functions, which is more general than the gH-derivative
The symmetric gradient of interval functions is more general and it is more robust for optimization problems
Summary
The optimization problems with uncertainty have received considerable attention and have great value in economic and control fields (e.g., [1,2,3,4]). The importance of derivatives in nonlinear interval-valued optimization problems can not be ignored. Toward this end, Wu [16,17,18]. According to the results given by Chalco-Cano [19], the gH-differentiability was extended to learn interval-valued KKT optimality conditions. Motivated by Wu [17] and Chalco-Cano [19], we introduce the gH-symmetrical derivative which is more general than the gH-derivative Based on this derivative and its properties, we give KKT optimality conditions for interval-valued optimization problems.
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