Optimization Letters ( IF 1.6 ) Pub Date : 2021-07-25 , DOI: 10.1007/s11590-021-01785-2 Xiangkai Sun 1 , Xinyi Feng 1 , Kok Lay Teo 2, 3
This paper is devoted to the investigation of a class of uncertain multiobjective fractional semi-infinite optimization problems (\(UMFP \), for brevity). We first obtain, by combining robust optimization and scalarization methodologies, necessary and sufficient optimality conditions for robust approximate weakly efficient solutions of (\(UMFP \)). Then, we introduce a Mixed type approximate dual problem for (\(UMFP \)) and investigate their robust approximate duality relationships. Moreover, we obtain some robust approximate weak saddle point theorems for an uncertain multiobjective Lagrangian function related to (\(UMFP \)).
中文翻译:
具有不确定数据的多目标分数半无限优化的鲁棒最优性、对偶性和鞍点
本文致力于研究一类不确定的多目标分数半无限优化问题(\(UMFP\),为简洁起见)。我们首先通过结合鲁棒优化和标量化方法,获得 ( \(UMFP\) ) 的鲁棒近似弱有效解的必要和充分最优条件。然后,我们为 ( \(UMFP \) )引入了一个混合型近似对偶问题,并研究了它们的稳健近似对偶关系。此外,我们为与 ( \(UMFP\) )相关的不确定多目标拉格朗日函数获得了一些鲁棒的近似弱鞍点定理。