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| Simplex-Algorithmus× | Benders-Zerlegung× | |
|---|---|---|
| Fachgebiet | Operations Research | Operations Research |
| Familie | Machine learning | Machine learning |
| Entstehungsjahr≠ | 1947 | 1962 |
| Urheber≠ | George Dantzig | Jacques F. Benders |
| Typ | algorithm | algorithm |
| Wegweisende Quelle≠ | Dantzig, G. B. (1963). Linear Programming and Extensions. Princeton University Press. DOI ↗ | Benders, J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238-252. DOI ↗ |
| Aliasnamen≠ | simplex algorithm | cutting plane method, constraint generation |
| Verwandt≠ | 4 | 3 |
| Zusammenfassung≠ | 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. | 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. |
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