Semivectorial bilevel programming versus scalar bilevel programming
Semivectorial bilevel programming versus scalar bilevel programming
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DOI：
10.1080/02331934.2019.1625900
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发表时间：
2020-04
期刊：
影响因子：
2.2
通讯作者：
S. Dempe;P. Mehlitz
中科院分区：
文献类型：
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作者：
S. Dempe;P. Mehlitz
本文考虑Banach空间中一类乐观半向量双层规划问题。假设相关的低级多标准优化问题是凸的其决策变量。这个性质意味着它的所有弱有效点都可以通过加权和标量化技术计算出来。因此，它是可能的，以取代整个半向量的双层规划问题的一个标准的双层规划问题，其上层变量包括一组合适的标量化参数为较低的水平问题。在这篇注记中，我们考虑这个代理双层规划问题和原来的半向量双层规划问题之间的关系。正如我们将要看到的，只要研究局部最优解，这就是一个微妙的问题。所得到的理论，以获得存在性结果的半向量双层规划问题，不一定是有限维的较低层次的决策变量。文中给出了二层最优控制的一些实例。
ABSTRACT We consider an optimistic semivectorial bilevel programming problem in Banach spaces. The associated lower level multicriteria optimization problem is assumed to be convex w.r.t. its decision variable. This property implies that all its weakly efficient points can be computed applying the weighted-sum-scalarization technique. Consequently, it is possible to replace the overall semivectorial bilevel programming problem by means of a standard bilevel programming problem whose upper level variables comprise the set of suitable scalarization parameters for the lower level problem. In this note, we consider the relationship between this surrogate bilevel programming problem and the original semivectorial bilevel programming problem. As it will be shown, this is a delicate issue as long as locally optimal solutions are investigated. The obtained theory is applied in order to derive existence results for semivectorial bilevel programming problems with not necessarily finite-dimensional lower level decision variables. Some regarding examples from bilevel optimal control are presented.