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?
With regards to slide 30, I believe that CPLEX offers both a reproducible (deterministic) as well as a non-reproducible (opportunistic) parallel solving modes. Gurobi does the same thing, but has a slightly different name for the relevant parameters.
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!
DeleteWith regards to slide 30, I believe that CPLEX offers both a reproducible (deterministic) as well as a non-reproducible (opportunistic) parallel solving modes. Gurobi does the same thing, but has a slightly different name for the relevant parameters.
ReplyDelete