向量最优化问题(包含多目标优化问题)是最优化研究中一类重要优化问题，鉴于这类优化问题有广泛的应用前景，其研究受到学界高度重视。向量优化问题的研究涉及向量比较大小，即序关系，因此研究向量优化问题有相当难度。目前研究向量优化问题的一个重要途径就是把向量优化问题转化为数值优化问题，通过数值优化问题的求解到达向量优化问题的求解，这种转化方式在向量优化问题的研究中称为向量优化问题的标量化。本项目集中探讨向量优化问题的标量化问题，主要探讨向量优化问题的线性标量化，非线性标量化和混合标量化。线性标量化主要解决凸性问题，非线性标量化主要解决非线性标量化函数的可微性和给出恰当的非凸分离定理，混合标量化问题主要解决标量化问题的统一性问题。

The class of vector optimization problems (including multiobjective optimization problem) is an important class of optimization problems in optimization. It is applicable to a wide range of real world practical problems. As a consequence, the area of vector optimization has attracted a great interest from among academic community. The need to deal with comparisons of vectors, i.e., sequence relations, is a great challenges in The study of vector optimization problems. Currently, an important approach being used is to transform a vector optimization problem into a numerical optimization problem. Then, the solution of the vector optimization problem can be obtained through solving the numerical optimization problem. This transformation method is called the scalarization of vector optimization problem in the research of vector optimization. The focus of this project is on the scalarization problems of vector optimization, which include linear scalarization, non-linear scalarization and mixed scalarization. Linear scalarization is mainly applied to solve convex optimization problems. For non-linear scalarization, its main application is in the solving of differentiability of non-linear scalarization function and providing appropriate non-convex separation theorems. On the other hand, the main focus of mixed scalarization is on the unification of scalarization problems.