I am a full-time consultant and provide services related to the design, implementation and deployment of mathematical programming, optimization and data-science applications. I also teach courses and workshops. Usually I cannot blog about projects I am doing, but there are many technical notes I'd like to share. Not in the least so I have an easy way to search and find them again myself. You can reach me at erwin@amsterdamoptimization.com.
sorry I think i meant the opposite, I was thinking that adding a new variable (for example x1 + x2 <= b, x1 + x2 >= a, letting z = x1 + x2) enlarges the final matrix system Ax <= b (x in vector form), to A'(x,z) <= b' (where A' now has one more dimension in column), thus A' is a larger matrix with more zeros, is that why this leads to a sparser matrix?
Thank you! I did not get why repeated expressions create denser models, is it because adding other variables make the vector of x larger?
ReplyDeleteDuplicate expressions lead to more nonzero elements. It does not "make the x vector larger".
Deletesorry I think i meant the opposite, I was thinking that adding a new variable (for example x1 + x2 <= b, x1 + x2 >= a, letting z = x1 + x2) enlarges the final matrix system Ax <= b (x in vector form), to A'(x,z) <= b' (where A' now has one more dimension in column), thus A' is a larger matrix with more zeros, is that why this leads to a sparser matrix?
DeleteYes. This can be seen from the model statistics for the different model formulations in the presentation.
DeleteI get it now, Thanks for the clarification!
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