Constrained optimization problems are relatively more complex than uncon-rnstrained optimization problems. Some of these complexities are minimizedrnby penalty and barrier methods. Penalty and barrier methods are approx-rnimating of constrained optimization problems by unconstrained optimiza-rntion problems or sequence of unconstrained optimization problem to _nd thernsolution of a given constrained optimization problem. In penalty functionrnmethod the constrained problem is replace by unconstrained (sequence ofrnunconstrained) problem by adding a term to the objective function that pre-rnscribes a high cost for violation of the constraints and in barrier methodrnthe problem is replaced by unconstrained (sequence of unconstrained) prob-rnlem through adding a term that favors points in the interior of the feasiblernregion over those near the boundary. Barrier requires that the interior ofrnthe feasible sets must be nonempty and therefore, they are used with prob-rnlems having only inequality constraints (there is no interior for equality con-rnstraints). Even though,these methods are fundamental, they have their ownrnseries limitations to _nd its approximate solution to the constrained prob-rnlem. In these methods we have to do with penalty parameter _, and thisrncertainly make problem of un-constraint optimization of the penalize objec-rntive function. With those limitations, method are very fundamentals to _ndrnbest solutions of constrained optimization problems with some restrictions.