Decomposition Methods for Large-Scale Optimization
Break large optimization problems into smaller subproblems using decomposition methods like Dantzig-Wolfe and Benders decomposition.
Some optimization problems are too large to solve directly—they might have millions of variables or constraints. Decomposition methods exploit problem structure by breaking them into smaller, more manageable pieces. Dantzig-Wolfe decomposition works when the constraint matrix has a special block structure. Benders decomposition separates problems into a master problem and subproblems, solving them iteratively. These methods don't just save computation time; they enable parallel processing where multiple subproblems solve simultaneously. Understanding decomposition helps you recognize when a monolithic model is intractable and guides you toward reformulating it in a way that your available solvers can handle.
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