The ( d + 1 ) inequalities can be turned into ( d + 1 ) equalities by introducing ( d + 1 ) slack variables.
12.
One way to obtain such a point is to relax the feasibility conditions using a slack variable; with enough slack, any starting point is feasible.
13.
The soft margin is the size of the margin separating positive from negative training instances minus positive slack variables that carry penalties for margin-violating samples.
14.
We have an LCP, due to the relation of complementarity between the slack variables " s " and their Lagrange multipliers " ? ".
15.
In an optimization problem, a "'slack variable "'is a variable that is added to an inequality constraint to transform it to an equality.
16.
As with the other variables in the augmented constraints, the slack variable cannot take on negative values, as the Simplex algorithm requires them to be positive or zero.
17.
Since each inequality can be replaced by an equality and a slack variable, this means each primal variable corresponds to a dual slack variable, and each dual variable corresponds to a primal slack variable.
18.
Since each inequality can be replaced by an equality and a slack variable, this means each primal variable corresponds to a dual slack variable, and each dual variable corresponds to a primal slack variable.
19.
Since each inequality can be replaced by an equality and a slack variable, this means each primal variable corresponds to a dual slack variable, and each dual variable corresponds to a primal slack variable.
20.
So if the " i "-th slack variable of the primal is not zero, then the " i "-th variable of the dual is equal to zero.
