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How to speed up the Mixed-Integer Quadratic Program process?

Computational Science Asked by hidemyname on September 17, 2020

Currently, I am solving a problem in the format:

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M is an integer as well. The problem that troubles me is that X is a vector in {0,1} with a size of 7000. I use the solver in https://github.com/oxfordcontrol/miosqp. It seems they are using the branch-and-bound algorithm. And they claim the speed is comparable to Gurobi. Is there a way to speed this calculation process up as it already took me 10 hours and I still can not get a solution. The parameters I can find to set the solver are the "integer feasibility tolerance", the "maximum number of iterations" and whether to use the "depth-first" rule or the "depth-first until the first incumbent and then best bound" rule.

I am totally new to the Mixed-Integer Quadratic Program so I don’t know what these parameters mean. Is there a way to speed it up if I don’t require a very accurate solution? Of course, I still don’t want to solution to be very bad. But I can tolerate the solver to get a solution within an hour.

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