Trust Region Newton Method With Two Dimensional Subspace Minimization
| dc.contributor.advisor | Guta, Berhanu (PhD) | |
| dc.contributor.author | Abye, Ageze | |
| dc.date.accessioned | 2019-04-23T07:14:13Z | |
| dc.date.accessioned | 2023-11-09T14:10:26Z | |
| dc.date.available | 2019-04-23T07:14:13Z | |
| dc.date.available | 2023-11-09T14:10:26Z | |
| dc.date.issued | 2018-05-03 | |
| dc.description.abstract | The trust region method, minimization of a real valued function f by using its quadratic model subject to Euclidean norm trust region constraint, occurs in many trust region algorithms. In most cases, it is inexpensive and even unnecessary to _nd an exact solution of a trust region problem unless the number of variables is relatively small. In order to alleviate this di_culty, in this thesis, we emphasized on a trust region method that takes Hessian of the model to be the true Hessian of a twice continuously di_erentiable real valued objective function f on Rn , at a given current iterate point xk using the so called two dimensional subspace minimization strategy. As the name indicates, the two dimensional subspace minimization method de_nes an approximate minimizer s to lie in a subspace Sk of Rn spanned by two reasonably chosen directions. We constructed such subspace using Lanczos iterative method. This subspace method _rst reduces the n-dimensional trust region problem to 2-dimensional constrained problem, and then to _nding roots of a fourth degree polynomial with the help of Lagrangian approach for constrained optimization problems. We compared the performance of the two dimensional subspace minimization method with that of an alternative trust region method, namely, the dogleg method, and the other common methods such as the steepest descent and Newton's method using MATLAB and we obtain that the two dimensional subspace minimization method is more e_cient. | en_US |
| dc.identifier.uri | http://10.90.10.223:4000/handle/123456789/18122 | |
| dc.language.iso | en | en_US |
| dc.publisher | Addis Ababa University | en_US |
| dc.subject | Optimization Problems | en_US |
| dc.subject | Lagrangian Method For Equality | en_US |
| dc.subject | Lagrangian Method For Inequality | en_US |
| dc.title | Trust Region Newton Method With Two Dimensional Subspace Minimization | en_US |
| dc.type | Thesis | en_US |