Optimization ( IF 2.2 ) Pub Date : 2020-11-12 , DOI: 10.1080/02331934.2020.1846189 Lahoussine Lafhim 1
ABSTRACT
In this work we adapt the main results from Khanh and Tung [First and second-order optimality conditions without differentiability in multivalued vector optimization. Positivity. 2015;19:817–841] for a general set-valued optimization problem to an optimistic bilevel set-valued programming problem as an optimization problem with implicitly given set-valued constraints. Using the optimal value function, we convert our problem into a one level set-valued optimization problem with general inequality constraints and derive both necessary conditions and sufficient conditions of order one and two. The main tools we exploit are approximations of set-valued mappings. To illustrate the obtained results, some examples are given.
中文翻译:
乐观双层集值规划中的一阶和二阶最优性条件
摘要
在这项工作中,我们采用了 Khanh 和 Tung [在多值向量优化中没有可微性的一阶和二阶最优条件的主要结果。积极性。2015;19:817–841] 将一般集值优化问题转换为乐观的双层集值规划问题,作为具有隐式给定集值约束的优化问题。使用最优值函数,我们将我们的问题转换为具有一般不等式约束的单级集值优化问题,并导出一阶和二阶的必要条件和充分条件。我们利用的主要工具是集值映射的近似值。为了说明获得的结果,给出了一些例子。