向量优化的理论、方法和应用

经济社会的高速发展出现的许多优化问题，大部分都是向量（多目标）优化问题。因此，向量优化问题的研究受到国内外运筹学专家的高度重视。本项目结合当前国际研究的前沿热点，针对向量优化问题今后发展趋势，重点研究变动偏序的向量优化问题，向量优化问题的近似解、真有效解与标量化，向量变分不等式与向量优化问题的关系以及随机多目标优化问题等相关理论、算法及应用。本项目的实施和完成不仅能够推动向量优化理论与算法的研究和实际中的应用，而且研究中发展起来的一些方法、技巧、工具以及研究结果对数学中的非线性分析、对策论、数理经济等的研究都将起到积极的推动作用。

Rapid development in economy and society has resulted in many challenging optimization problems being posed, and many of which are modelled as vector (multiobjective) optimization problems. Therefore, there is an urgent need to the study of vector optimization problems. The main tasks of this project are on the study of new theories,algorithms and their applications focusing on (i) vector optimization problems with Variable Ordering Structures;(ii) approximate solutions and proper efficient solutions in vector optimization problems; (iii) relationship between vector variational inequalities and vector optimization problems; and (iv) stochastic multiobjective optimization problems. These tasks will be accomplished based on state-of-the art results obtained by researchers among international research community and the trend for future development in vector optimization. The completion of this project will not only be of critical importance to the study of theories and algorithms of vector optimization and their applications, but will also represent a significant advancement in nonlinear mathematical analysis, game theory, and mathematical economics. .