A Vectorization Scheme for Nonconvex Set Optimization Problems
针对下集偏序关系下的集优化问题，提出一种向量化方案，通过构造多目标优化问题的参数族来逼近原问题的解集，并探讨了与多目标优化等价的特殊情形。
In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using established solvers from multiobjective optimization. Our strategy consists of deriving a parametric family of multiobjective optimization problems whose optimal solution sets approximate, in a specific sense, that of the set-valued problem with arbitrary accuracy. We also examine particular classes of set-valued mappings for which the corresponding set optimization problem is equivalent to a multiobjective optimization problem in the generated family. Surprisingly, this includes set-valued mappings with a convex graph.