ABSTRACT

In this paper, we investigate a multiobjectif bilevel programming problem with set valued constraints in both the upper problem and the lower problem. Using the notion of the support function to the feasible set mapping, together with an appropriate constraint qualification, we establish necessary optimality conditions in terms of asymptotical pointwise compact approximations; continuity of data functions and compactness of approximations are not necessarily required. In order to get sufficient optimality conditions, we introduce generalized pseudo-invexity and quasi-invexity notions in terms of asymptotical pointwise compact approximations. Examples that illustrate our results are given.

摘要

在本文中，我们研究了在上问题和下问题中都设置了值约束的多目标双层规划问题。使用支持函数的概念到可行集映射，加上适当的约束条件，我们根据渐近逐点紧逼逼近建立必要的最优性条件；不一定需要数据函数的连续性和近似的紧凑性。为了获得足够的最优条件，我们在渐近逐点紧逼逼近方面引入了广义伪invexity和quasi-invexity概念。给出了说明我们结果的例子。