Linear Programming - Restating a System as a Canonical Primal

[rockofeller]

Homework Statement

State the linear system Ax = b as a canonical minimum problem. What is the dual program?

Homework Equations

The canonical minimum problem is Ax = b, x\geq0, c\bulletx=min.

The Attempt at a Solution

I'm confused here, in part because there is no objective function c\bulletx=min. So far, I have:

define u_i\geq0, v_i\geq0, st. u_i - v_i=x_i \forallx_i\inx.

Then, if A is m\timesn, define a new matrix A^* with elements a^*_\alpha\beta = a_i(2j) for \beta even, a_{i(\frac{J+1}{2})} for \beta odd. Then A^* is an m\times2n matrix.

Then we define a new row vector x^* (whose transpose is) [u₁ v₁ \cdots u_n v_n]. Then x^* is 2n\times1 and our new constraints are A^*x^* = b, x^*\geq0.

Have I gotten this "right" so far? How do I come up with the new objective function?

 

[rockofeller]

Any ideas?