Re: [Bug-glpk] glp_warm_up

[Andrew Makhorin]

On Wed, 2013-03-06 at 19:17 -0600, David T. Price wrote:
> I don't understand your argument. Consider the problem:
> 
> Maximize 5 * x1
> 
> Bounds
> 1 <= x1 <= x2.
> 
> The trivial basis will put x1 on the boundary nearer 0, namely x1 = 1. 
> This is clearly primal feasible. However, the optimal solution of the 
> problem is x1 = 2. So the starting solution can't be dual feasible. 
> However, glp_warm_up says that the starting solution is "dual feasible" 
> and hence the status reported is "optimal". That is wrong.
> 
> Here are MPS and CPLEX forms of the input (I added "subject to -10 <= 
> x1" so that the problem would have a row), a fragment of test code, and 
> the output.
> 
> * Problem:
> * Class:      LP
> * Rows:       1
> * Columns:    1
> * Non-zeros:  1
> * Format:     Free MPS
> *
> NAME
> ROWS
>   N R0000000
>   G R0000001
> COLUMNS
>   C0000001 R0000000 5 R0000001 1
> RHS
>   RHS1 R0000001 -10
> BOUNDS
>   LO BND1 C0000001 1
>   UP BND1 C0000001 2
> ENDATA
> =====================================
> \* Problem: Unknown *\
> 
> Maximize
>   obj: + 5 x_1
> 
> Subject To
>   r_1: + x_1 >= -10
> 
> Bounds
>   1 <= x_1 <= 2
> 
> End
> =======================================
>      glp_warm_up(lpx);
> 
>      cout << "primal status: " << glp_get_prim_stat(lpx) << endl;
>      cout << "dual status: " << glp_get_dual_stat(lpx) << endl;
>      cout << "status: " << glp_get_status(lpx) << endl;
>      cout << "x1 = " << lpx_get_col_prim(lpx, 1) << endl;
> 
> ==========================================
> 
> primal status: 2
> dual status: 2
> status: 5
> x1 = 1
> 
> 

Thank you for your bug report. 

In fact, there is a bug in glp_warm_up, sorry. On checking the dual
feasibility it is necessary to check dual values depending on current
statuses of the variables, not on their types.

I will fix this in the next release.

Hope this bug is not crucial; in particular, the glpk simplex routines
ignore the status of starting solution.

Andrew Makhorin