Optimality conditions for the simple convex bilevel programming problem in Banach spaces
Optimality conditions for the simple convex bilevel programming problem in Banach spaces
复制标题
Banach空间中简单凸双层规划问题的最优性条件
DOI：
10.1080/02331934.2017.1394296
复制
发表时间：
2018
期刊：
影响因子：
2.2
通讯作者：
Pilecka
中科院分区：
文献类型：
--
作者：
Franke;Susanne;Mehlitz;Patrick;Pilecka
简单凸双层规划问题是一个凸极小化问题，其可行集是另一个凸优化问题的解集。在求某点在另一个方案解集上的投影时，这类问题经常出现。由于问题的性质，Slater的约束条件一般在任何可行点上都不成立。因此，为了陈述最优性条件，必须制定较弱的约束条件或平稳性概念。在本文中，我们使用问题的两种不同的单级重新表述，即最优值和Karush-Kuhn-Tucker方法，来推导原规划的最优性条件。由于所有这些考虑都是在Banach空间中进行的，因此结果并不局限于。在此基础上，我们引入并讨论了Banach空间中具有互补约束的数学规划的m -平稳性的概念。
The simple convex bilevel programming problem is a convex minimization problem whose feasible set is the solution set of another convex optimization problem. Such problems appear frequently when searching for the projection of a certain point onto the solution set of another program. Due to the nature of the problem, Slater’s constraint qualification generally fails to hold at any feasible point. Hence, one has to formulate weaker constraint qualifications or stationarity notions in order to state optimality conditions. In this paper, we use two different single-level reformulations of the problem, the optimal value and the Karush–Kuhn–Tucker approach, to derive optimality conditions for the original program. Since all these considerations are carried out in Banach spaces, the results are not limited to standard optimization problems in. On the road, we introduce and discuss a certain concept of M-stationarity for mathematical programs with complementarity constraints in Banach spaces.