পদ্ধতির তুলনা করুন

	বেন্ডার্স ডিকম্পোজিশন	অগমেন্টেড ল্যাগ্রাঞ্জিয়ান পদ্ধতি	কলাম জেনারেশন (ড্যান্টজিগ-উলফ)	সিমপ্লেক্স পদ্ধতি
ক্ষেত্র	পরিচালন গবেষণা	পরিচালন গবেষণা	পরিচালন গবেষণা	পরিচালন গবেষণা
পরিবার	Machine learning	Machine learning	Machine learning	Machine learning
উদ্ভবের বছর	1962	1969	1960	1947
প্রবর্তক	Jacques F. Benders	Magnus R. Hestenes and M. J. D. Powell	George B. Dantzig and Philip Wolfe	George Dantzig
ধরন	algorithm	algorithm	algorithm	algorithm
মৌলিক উৎস	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.	Dantzig, G. B., & Wolfe, P. (1960). Decomposition principle for linear programs. Operations Research, 8(1), 101-111.	Dantzig, G. B. (1963). Linear Programming and Extensions. Princeton University Press.
অপর নাম	cutting plane method, constraint generation	method of multipliers, augmented Lagrangian, ADMM	Dantzig-Wolfe decomposition, column generation method	simplex algorithm
সম্পর্কিত	3	3	3	4
সারসংক্ষেপ	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.	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 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.