0

I am learning about the Simplex Algorithm. I learned that we can turn an inequality constraint of the form $a_i x_i \leq b$ into an equality constraint $a_i x_i + s = b$ with $s \geq 0$. I do not know why and when should we do this?

Rodrigo de Azevedo
  • 23,223
ZonghanXU
  • 111
  • 1
    You should specify each notation you used in your post. Say what is $s$ here? And you need also to exhibit some of your ideas about understanding of the problem. – Shuchang Oct 28 '13 at 02:02

3 Answers3

1

If $a_ix_i\le b$ there will always be an $s\ge0$ such that $a_ix_i+s=b$.

As a lot of algorithms in linear programming require equality constraints, it is often useful in practice to make the conversions first before optimizing in earnest.

We call a linear program where all constrains are equality and all variables are non-negative to be in standard equality form.

Chiruno
  • 156
  • 7
1

I assume you haven't finished simplex learning. Simplex method require transform your initial problem to the standard form where every inequality becomes equality. You can find a lot of useful info about this method including online tools for your own simple tasks http://www.zweigmedia.com/RealWorld/simplex.html

Luke
  • 121
0

Simplex algorithm requieres equalities, so these variables called slack variables are used to transform inequalities into equalities.