Application Of Dogleg Method With Broyden Class Updating Technique For Solving Some Unconstrained Multivariate Nonlinear Optimization Problems:- Duru, Emmanuel C
ABSTRACT
In this work, the basic trust-region methods
for unconstrained multivariable nonlinear optimization problems were studied
using the Dogleg-type trust-region method which employed the Broyden Class
updating techniques in generating the approximation matrices to the Hessian of
the objective function. Specifically, for the Broyden class updating technique,
the values of the scalar parameter Qk as 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7,
0.8, 0.9 and 1 were used for each problem. The values of the initial
trust-region radius and the starting point of the decision variables were
varied at some points to observe the changes it may have on the solution. The
results obtained from the different updating class parameters were compared
taking note of the effects ofthe change in the solutions obtained for each
iteration. The results were compared with some known results obtained for the
same problems we considered and it shows that our method performed better at
some points and poorly at few points. It was discovered that the method
employed in this work is sensitive to the nature ofinitial points used as well
as slight changes in the value ofthe initial trust-region radius. The results
show that the value ofthe scalar parameter Qk = 0.1 performed relatively better
than others. Mathlab R2010a was used in executing the program.
0.0
DURU, D (2025). Application Of Dogleg Method With Broyden Class Updating Technique For Solving Some Unconstrained Multivariate Nonlinear Optimization Problems:- Duru, Emmanuel C. Repository.mouau.edu.ng: Retrieved May 21, 2025, from https://repository.mouau.edu.ng/work/view/application-of-dogleg-method-with-broyden-class-updating-technique-for-solving-some-unconstrained-multivariate-nonlinear-optimization-problems-duru-emmanuel-c-7-2
DURU, DURU. "Application Of Dogleg Method With Broyden Class Updating Technique For Solving Some Unconstrained Multivariate Nonlinear Optimization Problems:- Duru, Emmanuel C" Repository.mouau.edu.ng. Repository.mouau.edu.ng, 19 May. 2025, https://repository.mouau.edu.ng/work/view/application-of-dogleg-method-with-broyden-class-updating-technique-for-solving-some-unconstrained-multivariate-nonlinear-optimization-problems-duru-emmanuel-c-7-2. Accessed 21 May. 2025.
DURU, DURU. "Application Of Dogleg Method With Broyden Class Updating Technique For Solving Some Unconstrained Multivariate Nonlinear Optimization Problems:- Duru, Emmanuel C". Repository.mouau.edu.ng, Repository.mouau.edu.ng, 19 May. 2025. Web. 21 May. 2025. < https://repository.mouau.edu.ng/work/view/application-of-dogleg-method-with-broyden-class-updating-technique-for-solving-some-unconstrained-multivariate-nonlinear-optimization-problems-duru-emmanuel-c-7-2 >.
DURU, DURU. "Application Of Dogleg Method With Broyden Class Updating Technique For Solving Some Unconstrained Multivariate Nonlinear Optimization Problems:- Duru, Emmanuel C" Repository.mouau.edu.ng (2025). Accessed 21 May. 2025. https://repository.mouau.edu.ng/work/view/application-of-dogleg-method-with-broyden-class-updating-technique-for-solving-some-unconstrained-multivariate-nonlinear-optimization-problems-duru-emmanuel-c-7-2