两层多目标集值优化问题的最优性条件

Optimality Conditions for Bilevel Multiobjective Set Valued Optimization Problems

在集值分析的框架下，针对上、下层均为多目标且上层问题的集值函数是由下层问题的有效前沿隐性确定的这类两层多目标优化问题，建立了一个通用性结构化模型．研究了模型中构成函数的伴随导数、锥凸性、锥单调性和上局部Ｌｉｐｓｃｈｉｔｚ性．利用参数规划、非光滑分析和非线性分析的理论和方法。

This paper investigated the bilevel optimization problems with multiobjective in both upper level and lower level problems in the framework of set value analysis. It established a unified model to deal with the problems, where the set valued function of the upper level problem is determined implicitly by the efficient frontiers of the lower level problem. And then explored the contingent derivatives, cone convexity, cone monotonicity and upper locally Lipschitz property of the set valued functions involved in the model, respectively. Based on these and by the theories and methods of parametric programming, nonsmooth analysis and nonlinear analysis, the necessary and sufficient optimality conditions of cone efficient solutions for the model were obtained.