Abstract
In this paper, we first introduce the concept of interval-valued invex mappings by using gH-differentiability and compare it with interval-valued weakly invex mappings. We can observe that interval-valued invex mappings are more general than interval-valued weakly invex mappings. In addition, the sufficient optimality condition for interval-valued objective functions is derived under invexity.
Highlights
1 Introduction Convexity plays a vital role in many aspects of mathematical programming including, for example, sufficient optimality conditions and duality theorems
The concepts of preinvexity and invexity have been extended to intervalvalued functions by Zhang et al [ ], and the Kuhn-Tucker optimality conditions have been derived for preinvex and invex optimization problems with an interval-valued objective function under the conditions of weakly continuous differentiability and Hukuhara differentiability
The aim of this paper is to introduce the concept of invex intervalvalued mappings with gH-differentiable functions
Summary
Convexity plays a vital role in many aspects of mathematical programming including, for example, sufficient optimality conditions and duality theorems. The concepts of preinvexity and invexity have been extended to intervalvalued functions by Zhang et al [ ], and the Kuhn-Tucker optimality conditions have been derived for preinvex and invex optimization problems with an interval-valued objective function under the conditions of weakly continuous differentiability and Hukuhara differentiability.
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