Decomposition and distributed optimization

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Branch and price

Branch and price is an exact optimization algorithm combining branch-and-bound search with column generation, used for problems with exponentially many variables such as crew scheduling and vehicle routing.

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Column generation

Column generation is an optimization method that solves linear programs with very many variables by iteratively adding useful columns, used for cutting stock and vehicle routing.

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Constraint programming

Constraint programming is an approach where a problem is stated by constraints on decision variables, and a solver finds satisfying assignments by interleaving constraint propagation with systematic search.

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Cooperative optimization

Cooperative optimization is a global optimization method that decomposes a hard energy function into coupled subproblems, formulated by Xiaofei Huang in 2004 for computer vision labeling.

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Distributed constraint optimization

Distributed constraint optimization (DCOP) is a framework for multi-agent cooperation where agents control parts of a problem's variables and communicate by message passing to optimize a global objective.

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Dual decomposition

Dual decomposition is an optimization method that solves a large constrained problem by splitting it into subproblems coordinated through dual variables acting as prices, allowing parallel solution.

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Functional decomposition

Functional decomposition is a method that breaks a complex function into simpler subfunctions computed separately and recombined by composition, fundamental in logic synthesis and FPGA design.