本项目针对向量优化问题的近似解，重点研究向量优化问题的标量化刻画和二阶（高阶）对偶性，主要内容包括：（1）提出新的广义凸性，通过建立择一定理给出向量优化问题近似解的线性标量化刻画；（2）提出新的混合型标量化函数，探讨其基本性质，并建立向量优化问题近似解的等价性刻画；（3）探究Δ函数的新性质，给出向量优化问题近似解的非线性标量化刻画和最优性条件；（4）研究向量优化问题的二阶和高阶对偶性，重点是建立强对偶定理和逆对偶定理。本项目的实施和完成可以促进向量优化理论与方法的进一步发展。

This project mainly focuses on the study of scalarization and second-order (higher-order) duality for approximate solutions in vector optimization problems, which contain: (1) Some new classes of generalized convexity will be proposed, and then linear scalarization for approximate solutions of vector optimization problems will be given by establishing alternative theorem; (2) Some new combined scalarization functions will be presented, and equivalent characterizations of approximate solutions in vector optimization problems can be established after studying the basic properties of these functions; (3) By exploring new properties of function Δ, nonlinear scalarization and optimality conditions for approximate solutions in vector optimization problems will be obtained; (4) Second-order and higher-order duality results are developed for vector optimization problems, especially strong duality theorems and converse duality theorems. The implementation and accomplishment of this project can promote the development of vector optimization theory and methods.