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Can you provide numerical examples of primal and dual decomposition in mathematical optimization?

In my research on distributed control systems, I keep encountering these decomposition principles. While I understand the theory from textbooks, seeing a worked example with actual numbers would really solidify how the subproblems are formulated and coordinated. It's the bridge from theory to implementation that I'm missing.

 

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By Madhu B Answered 1 year ago

In my work on network resource allocation, I've implemented dual decomposition frequently. For a simple example, consider minimizing f1(x1) + f2(x2) subject to a shared constraint x1 + x2

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