Guta, Berhanu (PhD)Tefera, Liya2021-04-172023-11-042021-04-172023-11-042020-05-20http://etd.aau.edu.et/handle/123456789/26162Constrained 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.enConvex AnalysisUnconstrained OptimizationConstrained Op- TimizationPenalty MethodBarrier MethodsThesis