手法を比較

	ベンダー分解	Augmented Lagrangian Method
分野	オペレーションズ・リサーチ	オペレーションズ・リサーチ
系統	Machine learning	Machine learning
提唱年	1962	1969
提唱者	Jacques F. Benders	Magnus R. Hestenes and M. J. D. Powell
種類	algorithm	algorithm
原典	Benders, J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238-252.	Hestenes, M. R. (1969). Multiplier and gradient methods. Journal of Optimization Theory and Applications, 4(5), 303-320.
別名	cutting plane method, constraint generation	method of multipliers, augmented Lagrangian, ADMM
関連	3	3
概要	Benders Decomposition, introduced by Jacques F. Benders in 1962, is a powerful algorithmic framework for solving large-scale mixed-integer programming (MIP) problems. It decomposes the problem into a master problem (controlling complicating variables) and subproblems (handling remaining variables), using cutting planes generated from subproblem dual information to iteratively tighten the master problem.	The Augmented Lagrangian Method, developed by Magnus R. Hestenes and M. J. D. Powell in 1969, is a powerful technique for solving constrained optimization problems. It converts a constrained problem into a sequence of unconstrained subproblems by augmenting the Lagrangian with a quadratic penalty term, enabling efficient solution of large-scale problems including convex and nonconvex cases.