[Osi] dual bound on the primal

kmt123 at mac.com kmt123 at mac.com
Wed Oct 20 12:30:09 EDT 2010


I understand your first point.

I think I only partially understand your second point.  I don't quite understand how to apply what you said.

I know the optimal dual objective value (it's the same as the primal, via strong duality).  Since I am changing only the column bounds (i.e. l <= x <= u) it seems what I need is the the corresponding changes to the dual objective value.
Is that dual objective value change a function of the reduced costs (this makes since to me)?  I know it's a function of the the column upper and lower bounds (l and u) and it's a dot product.  Maybe this comes down to how the column bounds are converted to standard form in OSI.

Is this the change in the dual objective function due to the column bounds change?
-cBar(of nonbasic variables) * (u - l)

Kyle

On Oct 20, 2010, at 9:18 AM, Lou Hafer wrote:

> Kyle,
> 
> 	Range constraints L <= ax <= U are transformed into a single constraint
> ax + s = U with a bounded slack 0 <= s <= (U-L).
> 
> 	Duals of nonbasic bounded variables are the negative of the reduced
> costs.
> 
> 						Lou
> 
> 
> 
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