方法对比

	列生成算法 (Dantzig-Wolfe)	增广拉格朗日方法	单纯形法
领域	运筹学	运筹学	运筹学
方法族	Machine learning	Machine learning	Machine learning
起源年份	1960	1969	1947
提出者	George B. Dantzig and Philip Wolfe	Magnus R. Hestenes and M. J. D. Powell	George Dantzig
类型	algorithm	algorithm	algorithm
开创性文献	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.	Dantzig, G. B. (1963). Linear Programming and Extensions. Princeton University Press.
别名	Dantzig-Wolfe decomposition, column generation method	method of multipliers, augmented Lagrangian, ADMM	simplex algorithm
相关	3	3	4
摘要	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.	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.