Abstract
The main objective of this paper is to investigate the generalized convexity of interval-valued functions under the total order relation and apply it to a class of unconstrained interval-valued optimization problems. For this purpose, we present the new definition of preinvex interval-valued functions and obtain its several fascinating characterizations. Then, we introduce the $\preceq_{cw}$-semicontinuity and discuss its relationship with preinvex interval-valued functions. As applications related to preinvex interval-valued functions, we study a class of unconstrained interval-valued optimization problems and discuss the existence theorem of its optimal solution.
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