Application Of Dogleg Method With Broyden Class Updating Technique For Solving Some Unconstrained Multivariate Nonlinear Optimization Problems

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  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 of the 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 of initial points used as well as slight changes in the value of the initial trust-region radius. The results show that the value of the scalar parameter  performed relatively better than others. Mathlab R2010a was used in executing the program.