Exterior Penalty Method

Exterior Penalty method

Algorithm. The exterior penalty function method can be stated by the following steps:
1. Start from any design X1 and a suitable value of r1. Set k = 1.
2. Find the vector X∗k that minimizes the function
𝜙(X, rk) = f (X) + rk
Σm
j=1
⟨gj(X)⟩q
3. Test whether the point X∗k satisfies all the constraints. If X∗k is feasible, it is the
desired optimum and hence terminates the procedure. Otherwise, go to step 4.
4. Choose the next value of the penalty parameter that satisfies the relation
rk+1 > rk
and set the new value of k as original k plus 1 and go to step 2. Usually, the
value of rk+1 is chosen according to the relation rk+1 = crk, where c is a constant
greater than 1.