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| Augmented Lagrangian Method× | 列生成法（ダンツィグ・ウルフ法）× | |
|---|---|---|
| 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≠ | 1969 | 1960 |
| 提唱者≠ | Magnus R. Hestenes and M. J. D. Powell | George B. Dantzig and Philip Wolfe |
| 種類 | algorithm | algorithm |
| 原典≠ | Hestenes, M. R. (1969). Multiplier and gradient methods. Journal of Optimization Theory and Applications, 4(5), 303-320. DOI ↗ | Dantzig, G. B., & Wolfe, P. (1960). Decomposition principle for linear programs. Operations Research, 8(1), 101-111. DOI ↗ |
| 別名≠ | method of multipliers, augmented Lagrangian, ADMM | Dantzig-Wolfe decomposition, column generation method |
| 関連 | 3 | 3 |
| 概要≠ | 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. |
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