拉格朗日松弛
拉格朗日
计算理论
放松(心理学)
数学优化
计算机科学
整数规划
分解
对偶(语法数字)
水准点(测量)
整数(计算机科学)
工作(物理)
数学
应用数学
算法
物理
心理学
社会心理学
生态学
艺术
文学类
大地测量学
生物
程序设计语言
地理
热力学
标识
DOI:10.1007/s10479-023-05499-9
摘要
Operations in areas of importance to society are frequently modeled as mixed-integer linear programming (MILP) problems. While MILP problems suffer from combinatorial complexity, Lagrangian Relaxation has been a beacon of hope to resolve the associated difficulties through decomposition. Due to the non-smooth nature of Lagrangian dual functions, the coordination aspect of the method has posed serious challenges. This paper presents several significant historical milestones (beginning with Polyak’s pioneering work in 1967) toward improving Lagrangian Relaxation coordination through improved optimization of non-smooth functionals. Finally, this paper presents the most recent developments in Lagrangian Relaxation for fast resolution of MILP problems. The paper also briefly discusses the opportunities that Lagrangian Relaxation can provide at this point in time.
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