随机多目标优化是多目标优化和随机优化的结合，在经济、管理和机器学习等诸多领域有着广泛的应用。随着机器学习的快速发展，随机多目标优化已成为最优化领域的研究热点。但是，与多目标优化和随机优化相比，随机多目标优化（特别是算法）的研究还处于初级阶段。特别地，当随机变量的分布未知或者难以得到期望值函数的显示表达式时，多目标优化和随机优化的分析和算法工具均无法直接解决这类问题。本项目拟研究随机多目标优化的有效算法。主要研究内容包括：基于随机一阶信息的算法、基于随机二阶信息的算法及在不依赖于标量化参数的情况下的样本均值逼近方法，建立上述算法的收敛性理论，并将其应用于经济、管理和机器学习中实际问题的分析与求解。本项目的实施和完成可以丰富和发展随机多目标优化的算法和应用。

Stochastic multiobjective optimization is a combination of multiobjective optimization and stochastic optimization, which is widely used in many fields such as economy, management and machine learning. With the rapid development of machine learning, stochastic multiobjective optimization has been intensively investigated by many researchers in the field of optimization. However, compared with multiobjective optimization and stochastic optimization, the methodological and theoretical development of stochastic multiobjective optimization algorithms remains in its infancy. In particular, the analytical and algorithmic tools from multiobjective optimization and stochastic optimization cannot directly resolve this kind of problem when the distribution of random variable is unknown or it is difficult to obtain a closed form of the expected value of random functions. Therefore, the aim of this project is to study the effective algorithms for stochastic multiobjective optimization, which contains: we will study the algorithm based on stochastic first-order information, the algorithm based on stochastic second-order information, and sample average approximation methods without the scalarization parameters. We will establish the convergence theory of the above algorithms and apply them to analyze and solve practical problems arise in economy, management and machine learning. The implementation and accomplishment of this project can enrich and develop the algorithms and applications of stochastic multiobjective optimization.