R.Deumlich, habiI.(AssociateProfessor)Gidey, Tadesse2021-12-232023-11-042021-12-232023-11-042005-07http://etd.aau.edu.et/handle/123456789/29418In this thesis, we deal with a theoretical basis of optimization in general and on numerical methods in particular. Here the penalty methods are in the foreground . Some generalizations for theorems into arbitrary metric space with mild assumptions (Theorem 2.1.3 and 3.1.3) are done. In addition, a numerical computation is presented and tested, with the code written in Mathematica 4.1 . Comparisons are made for different choice of the penalty function with respect to convergence speed and objective value.enOn the Penalty Method In Optimization;Thesis