How can I significantly improve the speed of this linear programming problem in JuMP?

Specific Domains Optimization (Mathematical)
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8

Hi odow,

Your code indeed improves the speed a lot. I really appreciate it. However, there is a glitch in function solve_lower_bound. After I add the following code, the speed is basically the same as my original code, is there another way to write this code?

    if has_upper_bound(model_lb[:lambda_sum][i, j])
        delete_upper_bound(model_lb[:lambda_sum][i, j])
    end

    if has_lower_bound(model_lb[:lambda_sum][i, j])
        delete_lower_bound(model_lb[:lambda_sum][i, j])
    end

Without the above code, it solves 10 problem for N=500 in 9 seconds, after I add the above code, the time is nearly doubled. I am not sure why the new code will take so much time.

The reason I need the above code is as follows. For one iteration, it puts bounds on all lambda_sum[i_lb, j_lb] except for lambda_sum[i, j]. In the next iteration, say that we are going to solve for W[i',j'], so that there should be no bounds on W[i',j']. However, the bounds put on W[i',j'] in the previous iteration are still there. Therefore, I add the following codes to clear bounds before the for-loop in function solve_lower_bound.

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