手法を比較

	シンプレックス法	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	1947	1969
提唱者	George Dantzig	Magnus R. Hestenes and M. J. D. Powell
種類	algorithm	algorithm
原典	Dantzig, G. B. (1963). Linear Programming and Extensions. Princeton University Press.	Hestenes, M. R. (1969). Multiplier and gradient methods. Journal of Optimization Theory and Applications, 4(5), 303-320.
別名	simplex algorithm	method of multipliers, augmented Lagrangian, ADMM
関連	4	3
概要	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.	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.