Re: [Help-glpk] dual simplex and re-optimization when only variable's bounds change

[Andrew Makhorin]

> I just want to verify my understanding about calling dual simplex and
> re-optimization.

> My problem is to solve many LP of the following form:

> max/min  x_k
> s.t.
>   A*x = b
>   l <=  x  <= u

> for k=1,2,...,n. (x is R^n)

> For each LP, only the boundary of x (i.e., l, u) are changed.

> I set glpk parameter to use DUALP and presolve is OFF.

> Then I call glpk to solve the above LP with different bounds.

> Is this the correct step ?

Yes. In this case the glpk simplex solver will start new search from
the current basis, which was optimal before you changed bounds.

> Is there any other calling sequence that can help reducing the total 
> number of simplex iterations ?

Once you have solved your instance to optimality for the first time,
you can save the optimal basis, i.e. row/column statuses reported by
glp_get_row_stat and glp_get_col_stat. Then every time you change
bounds, you can restore the initial basis using glp_set_row_stat and
glp_set_col_stat before performing re-optimization. In this case
glp_simplex will always start from the initial basis.