ABSTRACT

This paper deals with robust ε-quasi optimal solutions for a class of nonsmooth optimization problems with uncertain data. Under some mild assumptions, we first establish, by using robust optimization (i.e. worst-case) approach, approximate optimality conditions for this uncertain nonsmooth optimization problem. Then, we introduce a Mixed-type robust approximate dual problem of this uncertain optimization problem, and explore their relationships. Moreover, using a scalarization method, we derive optimality conditions for robust weakly approximate efficient solutions for an uncertain nonsmooth multiobjective optimization problem. We also obtain approximate duality theorems for the uncertain nonsmooth multiobjective optimization problem.

摘要

本文针对一类具有不确定数据的非光滑优化问题，提出了鲁棒的ε-拟最优解。在一些温和的假设下，我们首先通过使用稳健的优化（即最坏情况）方法来为该不确定的非光滑优化问题建立近似最优条件。然后，我们介绍了该不确定优化问题的混合型鲁棒近似对偶问题，并探讨了它们之间的关系。此外，使用标化方法，我们得出了不确定的非光滑多目标优化问题的鲁棒弱近似有效解的最优性条件。我们还获得了不确定的非光滑多目标优化问题的近似对偶定理。