Optimality Condition for Smooth Constrained Optimization Problems
| dc.contributor.advisor | Guta, Berhanu (PhD) | |
| dc.contributor.author | Tafa, Meta | |
| dc.date.accessioned | 2021-03-25T06:12:40Z | |
| dc.date.accessioned | 2023-11-04T12:31:12Z | |
| dc.date.available | 2021-03-25T06:12:40Z | |
| dc.date.available | 2023-11-04T12:31:12Z | |
| dc.date.issued | 2020-08-30 | |
| dc.description.abstract | Mathematical optimization is the process of maximizing or minimizing an objective function by _nding the best available values across a set of inputs under a restriction domain. This project focuses on _nding the optimality condition for optimization problems of di_erentiable function. For unconstrained optimization problems, checking the positive de_niteness of the Hessian matrix at stationary points, one can conclude whether those stationary points are optimum points or not, if the objective function is di_erentiable. For constrained Optimization problem, the objective function and the function in the constraint sets are di_erentiable and the well known optimality condition called Karush-Kuhn-Tucker (KKT) condition leads to _nd the optimum point(s) of the given optimization problem and the convetional Lagrangian approach to solving constrained optimization problems leads to optimality conditions which are either necessary or su_cient, but not both unless the underlying objective functions and functions in constraints set are also convex. The Tchebyshev norm leads to an optimality conditions which is both su_cient and necessarly without any convexity assumption.This optimality conditions can used to device a conceptually simple method for solving non-convex inequality constrained optimization problems. | en_US |
| dc.identifier.uri | http://etd.aau.edu.et/handle/123456789/25666 | |
| dc.language.iso | en | en_US |
| dc.publisher | Addis Ababa University | en_US |
| dc.subject | Convex Set | en_US |
| dc.subject | Convex Function | en_US |
| dc.subject | Constrained Optimization | en_US |
| dc.subject | Inequality Constraints | en_US |
| dc.subject | Equality Constraints | en_US |
| dc.subject | Smooth Optimization | en_US |
| dc.subject | Positive De_Niteness | en_US |
| dc.subject | Hessian Matrix | en_US |
| dc.subject | Non-Convex Optimization | en_US |
| dc.subject | Equivalent Optimality Conditions | en_US |
| dc.subject | Unconstrained Optimization | en_US |
| dc.title | Optimality Condition for Smooth Constrained Optimization Problems | en_US |
| dc.type | Thesis | en_US |