Re: Obtaining the primal solution after using dual simplex method

From: Tuomo Takkula (tuomo_at_zsh.cs.chalmers.se)
Date: 12/10/04 

Date: 10 Dec 2004 14:03:47 +0100

acwkhk@yahoo.com.hk (alexchan) writes:

> Hi there!
>
> I am currently studying on the duality in LP, and I've read that the
> dual simplex method can solve the dual solution from the original LP
> problem. But it seems that I am only interested in the primal
> solution. Can anyone teach me how to obtain the primal solution set
> form the dual solution?

You have an optimal basis. What else do you need?

> I've also read about the Lagrange multiplyer ...

Dual optimal variables are Lagrange multipliers - so far, so
correct. Considering the Lagrangian dual, of course the Lagrange
subproblem wrt to optimal multipliers gives you a feasible (and hence
optimal) primal solution, since LP problems are convex optimization
problems over closed convex sets.

> .. but that doesn't help with this case since it cannot give me the
> exact solution.

Nonsense. You may use the Lagrangian dual of you insist - but you
already gave an optimal basis, which is certainly enough.

        Cheers
        Tuomo