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Optimality conditions for pessimistic bilevel problems using convexificator
Positivity ( IF 0.8 ) Pub Date : 2020-02-11 , DOI: 10.1007/s11117-020-00737-x S. Dempe , N. Gadhi , L. Lafhim
中文翻译:
使用凸化器的悲观双层问题的最优性条件
更新日期:2020-02-11
Positivity ( IF 0.8 ) Pub Date : 2020-02-11 , DOI: 10.1007/s11117-020-00737-x S. Dempe , N. Gadhi , L. Lafhim
The purpose of this paper is to study the pessimistic version of bilevel programming problems in finite-dimensional spaces. Problems of this type are intrinsically nonsmooth (even for smooth initial data). By using optimal value function, we transform the initial problem into a generalized minimax optimization problem. Using convexificators, first-order necessary optimality conditions are then established. An example that illustrates our findings is also given.
中文翻译:
使用凸化器的悲观双层问题的最优性条件
本文的目的是研究有限维空间中双层规划问题的悲观版本。这种类型的问题本质上是不平滑的(即使对于平滑的初始数据而言)。通过使用最优值函数,我们将初始问题转换为广义的minimax优化问题。然后使用凸化器建立一阶必要最优条件。还给出了一个说明我们的发现的示例。