# multi-stage bender's decomposition with overlapping y variables

 3 2 From my textbook, I learned bender's decomposition for 2-stage problems and the y variables is non-overlapping. Indeed, I wish to look into this decomposition further since it is very likely a solution to two of my difficult LPs: but from the textbook, its structural is not exactly what my problem is since its y-variable is not overlapping: To address my problem, I hope that there is a version of bender's decomposition with overlapping y variables. Do you have some recommendation (books) that I could look into? Thank you:) asked 18 Oct '14, 13:59 Chivalry 229●3●19 accept rate: 0%

 5 Are your $$x$$ variables integer-valued? If not, I'm not sure why you would want to use Benders, which is designed for master problems that are MILPs (or, I think, NLPs). If your mission is just to decompose a large LP into smaller LPs, you might want to look into Dantzig-Wolfe decomposition. If the number of "overlapping" variables between any two blocks is relatively small, you might try the following trick. Suppose that $$y_k$$ belongs to two blocks. Create a clone $$y_{k}'$$, substitute $$y_{k}'$$ for $$y_k$$ in one block but not the other, and add a constraint $$y_k = y_{k}'$$ to the master problem. answered 18 Oct '14, 14:51 Paul Rubin ♦♦ 14.6k●5●13 accept rate: 19% Thank you very much for hinting me on that... I would try that :) (18 Oct '14, 16:16) Chivalry
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