不确定数学规划的鲁棒可行半径:综述与最新进展

The radius of robust feasibility of uncertain mathematical programs: A Survey and recent developments

European Journal of Operational Research · 2021
被引 12
ABS 4

中文导读

综述了不确定数学规划中鲁棒可行半径的研究现状,涵盖连续、混合整数、半无限、凸约束及锥线性约束程序,并分析其与病态距离的联系,帮助研究者快速了解该工具。

Abstract

The radius of robust feasibility provides a numerical value for the largest possible uncertainty set that guarantees feasibility of a robust counterpart of a mathematical program with uncertain constraints. The objective of this review of the state-of-the-art in this field is to present this useful tool of robust optimization to its potential users and to avoid undesirable overlapping of research works on the topic as those we have recently detected. In this paper we overview the existing literature on the radius of robust feasibility in continuous and mixed-integer linearly constrained programs, linearly constrained semi-infinite programs, convexly constrained programs, and conic linearly constrained programs. We also analyze the connection between the radius of robust feasibility and the distance to ill-posedness for different types of uncertain mathematical programs.

鲁棒优化数学规划可行性分析不确定性建模