This paper is devoted to constructing Wolfe and Mond–Weir dual models for interval-valued pseudoconvex optimization problem with equilibrium constraints, as well as providing weak and strong duality theorems for the same using the notion of contingent epiderivatives with pseudoconvex functions in real Banach spaces. First, we introduce the Mangasarian–Fromovitz type regularity condition and the two Wolfe and Mond–Weir dual models to such problem. Second, under suitable assumptions on the pseudoconvexity of objective and constraint functions, weak and strong duality theorems for the interval-valued pseudoconvex optimization problem with equilibrium constraints and its Mond–Weir and Wolfe dual problems are derived. An application of the obtained results for the GA-stationary vector to such interval-valued pseudoconvex optimization problem on sufficient optimality is presented. We also give several examples that illustrate our results in the paper.

中文翻译：

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具有平衡约束的区间值伪凸优化问题的对偶结果及应用

本文致力于构造具有均衡约束的区间值伪凸优化问题的Wolfe和Mond-Weir对偶模型，并使用在实际Banach空间中具有伪凸函数的或有表生导数的概念为其提供弱和强对偶定理。首先，我们介绍了Mangasarian-Fromovitz型正则条件以及针对这种问题的两个Wolfe和Mond-Weir对偶模型。其次，在对目标函数和约束函数的伪凸性进行适当假设的基础上，推导了带有平衡约束的区间值伪凸优化问题及其Mond-Weir和Wolfe对偶问题的弱对偶对偶定理。提出了将遗传算法平稳向量的所得结果应用于具有足够最优性的区间值伪凸优化问题。我们还提供了一些示例来说明本文的结果。