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Optimality conditions and duality results for generalized-Hukuhara subdifferentiable preinvex vector interval optimization problems
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  • Zaiyun Peng,
  • Jian-Yi Peng,
  • Dan Li,
  • Yong Zhao
Zaiyun Peng
Chongqing Jiaotong University

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Jian-Yi Peng
Chongqing Jiaotong University
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Dan Li
Chongqing Jiaotong University
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Yong Zhao
Chongqing Jiaotong University
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Abstract

In this paper, a class of preinvex vector interval optimization problems (VIOP) with gH-subdifferential is considered, and the optimality conditions and dual results are gained. Firstly, the definition of subgradient for preinvex interval valued function under gH-difference is given, and examples are given to verify the difference between the subgradient in this paper and the subgradient in[28]. Secondly, by means of gH-subdifferential, the Karush-Kuhn-Tucker sufficient and necessary conditions for preinvex (VIOP) are studied. Then, the Mond-Weir dual problem and Wolfe dual problem of preinvex (VIOP) are established, furthermore, weak duality, strong duality, and converse duality theorems are obtained by using the gH-subdifferential. Some examples are given to illustrate the main results. To some extent, the main results generalize the existing relevant results.