Testing optimality via complementary slackness

[zfolwick]

I can't for the life of me understand this topic. given a point x =(1,1,1,1,1,1,1) and a primal LP, does the point solve the primal? An internet search revealed no answer to my question, only criteria which involves knowing y. I am aware that \suma_ijx_j < b then y_i = 0, so I at least know which elements of y are zero, but the rest of the steps elude me.

 

[lavinia]

I can't for the life of me understand this topic. given a point x =(1,1,1,1,1,1,1) and a primal LP, does the point solve the primal? An internet search revealed no answer to my question, only criteria which involves knowing y. I am aware that \suma_ijx_j < b then y_i = 0, so I at least know which elements of y are zero, but the rest of the steps elude me.

you need to be more clear. Explain in more detail.

 

[zfolwick]

given a point x =(a₁, a₂, ... a_m), is this point optimal for a given LP?

Is there a good, step-by-step description of this somewhere? The only thing I can find is that, if I have a point x and a point y, then I can use the weak duality theorem to say that cx = by or some such nonsense.

what I'm really trying to understand is the pivoting process wherein I *get* y from a given point x.