向量优化及其若干进展

摘要/Abstract

摘要： 在一定的约束条件下极小化或极大化向量值函数，这就是向量优化. 向量优化是数学规划学科中的重要分支学科，是具有重要应用价值的、新兴的和多学科交叉的研究领域. 自1950年以来，已经逐步形成较完整的理论体系，算法研究也有一定的进展，应用日渐广泛. 简述了它的发展历程、主要特征、基本理论和方法，综述了国内学者近几年来在若干领域的发展状况和主要代表性成果，展望了向量优化学科未来的发展方向.

关键词: 向量优化, 学科概述, 学科发展现状, 研究展望

Abstract: Vector optimization is a mathematical model which minimizes or maximizes a vector-valued function. As an important part of mathematical programming, vector optimization is a promising interdisciplinary research field with many significant applications. Since 1950, the structure of the theory of vector optimization has been very complete, as well as some important progresses have been made in the study of methods, furthermore the applications have been flourishing. In this paper, we briefly review the developments of vector optimization, introduce the main characteristics, the basic theory and methods of it, highlight some recent typical progresses achieved by Chinese researchers, and propose some possible research prospects in future.

Key words: vector optimization, overview of subjects, present situation of academic development, research prospects

中图分类号:

O221，O224

戎卫东，杨新民. 向量优化及其若干进展[J]. 运筹学学报, 2014, 18(1): 9-38.

RONG Weidong, YANG Xinmin. Vector optimization and its developments[J]. Operations Research Transactions, 2014, 18(1): 9-38.

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