Penalty and Barriers Methods for Constrained Optimization Problems
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Date
2020-05-20
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Addis Ababa University
Abstract
Constrained optimization problems are relatively more complex than uncon-
strained optimization problems. Some of these complexities are minimized
by penalty and barrier methods. Penalty and barrier methods are approx-
imating of constrained optimization problems by unconstrained optimiza-
tion problems or sequence of unconstrained optimization problem to _nd the
solution of a given constrained optimization problem. In penalty function
method the constrained problem is replace by unconstrained (sequence of
unconstrained) problem by adding a term to the objective function that pre-
scribes a high cost for violation of the constraints and in barrier method
the problem is replaced by unconstrained (sequence of unconstrained) prob-
lem through adding a term that favors points in the interior of the feasible
region over those near the boundary. Barrier requires that the interior of
the feasible sets must be nonempty and therefore, they are used with prob-
lems having only inequality constraints (there is no interior for equality con-
straints). Even though,these methods are fundamental, they have their own
series limitations to _nd its approximate solution to the constrained prob-
lem. In these methods we have to do with penalty parameter _, and this
certainly make problem of un-constraint optimization of the penalize objec-
tive function. With those limitations, method are very fundamentals to _nd
best solutions of constrained optimization problems with some restrictions.
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Keywords
Convex Analysis, Unconstrained Optimization, Constrained Op- Timization, Penalty Method, Barrier Methods