基于预不变凸区间值优化问题的最优性条件

Optimality Conditions for Preinvex Interval-Valued Optimization Problems

摘要: 现有模糊优化相关研究中，最优性条件多围绕伪不变凸函数展开，而预不变凸场景下的区间值优化最优性条件尚未得到充分探讨，存在研究空白。基于此，本文引入预不变凸区间值函数，明确其与可微性的关联，构建预不变凸环境下的区间值优化模型，推导可微条件下的最优性充分与必要条件，既完善区间值优化的理论体系，也为模糊优化问题的求解提供间接的理论支撑。

Abstract: In existing research on fuzzy optimization, optimality conditions are mostly centered on pseudoinvex functions, while the optimality conditions for interval-valued optimization under the preinvex scenario have not been fully explored, leaving a research gap. Based on this, this paper introduces the preinvex interval-valued function, clarifies its connection with differentiability, establishes an interval-valued optimization model under the preinvex framework, and derives the sufficient and necessary optimality conditions under differentiable conditions. This not only improves the theoretical system of interval-valued optimization but also provides indirect theoretical support for solving fuzzy optimization problems.