A constrained minimization problem in standard format 
min f_{0}(x) 
x in X 
s.t. g_{j}(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)=f_{0}(x)+r_{p}Sum{max(0,g_{j})^{2}}, j=1,...,m 
x in X 
The measure of constraint violation, Sum{max(0,g_{j})^{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:
r_{p+1}=cr_{p} 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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