From my textbook, I learned bender's decomposition for 2stage problems and the y variables is nonoverlapping. Indeed, I wish to look into this decomposition further since it is very likely a solution to two of my difficult LPs: https://www.orexchange.org/questions/10340/methodofseparationforlpswithexponentiallymanyconstraints https://www.orexchange.org/questions/10401/simultaneouscolumnandrowgenerationreference but from the textbook, its structural is not exactly what my problem is since its yvariable 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 
Are your \(x\) variables integervalued? 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 DantzigWolfe 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 ♦♦ Thank you very much for hinting me on that... I would try that :)
(18 Oct '14, 16:16)
Chivalry
