A constrained minimization problem in standard format |
min f0(x) |
x in X |
s.t. gj(x), j=1,...,m |
can be solved using an exterior penalty formulation in which a penalty is imposed for each constraint violation. |
The resulting penalty formulation is as follows: |
min F(x)=f0(x)+rpSum{max(0,gj)2}, j=1,...,m |
x in X |
The measure of constraint violation, Sum{max(0,gj)2},
j=1,...,m has a value equal to zero in the feasible region, and a positive
value when any constraint is violated. Here, the variable penalty approach
is adopted to iteratively increase the penalty factor.
This program allows a user to specify an initial value for the penalty factor, or choose a default value: |
|
The variable penalty factor is updated according to the following schedule:
rp+1=crp where the updating constant c, and the number of iterations between each penalty iteration may be specified by the user, or set to default values: |
default number of iterations between two consecutive penalty iterations = 100. |
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