Порівняння методів

	Генерація стовпців (Данциг-Вольф)	Метод доповненого лагранжіана	Декомпозиція Бендерса	Метод симплекс
Галузь	Дослідження операцій	Дослідження операцій	Дослідження операцій	Дослідження операцій
Родина	Machine learning	Machine learning	Machine learning	Machine learning
Рік появи	1960	1969	1962	1947
Автор методу	George B. Dantzig and Philip Wolfe	Magnus R. Hestenes and M. J. D. Powell	Jacques F. Benders	George Dantzig
Тип	algorithm	algorithm	algorithm	algorithm
Основоположне джерело	Dantzig, G. B., & Wolfe, P. (1960). Decomposition principle for linear programs. Operations Research, 8(1), 101-111.	Hestenes, M. R. (1969). Multiplier and gradient methods. Journal of Optimization Theory and Applications, 4(5), 303-320.	Benders, J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238-252.	Dantzig, G. B. (1963). Linear Programming and Extensions. Princeton University Press.
Інші назви	Dantzig-Wolfe decomposition, column generation method	method of multipliers, augmented Lagrangian, ADMM	cutting plane method, constraint generation	simplex algorithm
Пов'язані	3	3	3	4
Підсумок	Column Generation, developed by George B. Dantzig and Philip Wolfe in 1960, is a powerful optimization technique for solving large-scale linear programming problems with special structure. Also known as Dantzig-Wolfe Decomposition, it decomposes the problem into a master problem (restricted to a subset of variables/columns) and a pricing subproblem (identifying new variables), iteratively improving the solution by introducing only relevant columns.	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.	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 Simplex Method, developed by George Dantzig in 1947, is a foundational algorithm for solving linear programming problems. It systematically explores vertices of the feasible region to find the optimal solution where the objective function is maximized or minimized subject to linear constraints.