Abstract:
Trust region method is an important class of iterative methods for the solution of nonlinear
optimization problems. This project considers nonlinear unconstrained convex optimization
problems in which the objective functions are diffentiable. To solve such type of problems, trust
region method was used and applied to construct model of the objective function during the
optimization process. This approach was based on building a quadratic model which reasonably
reflects the local behavior of the original objective function in a sub region. It approximately
minimized the model of the true objective function within a trust region for which a suitable
norm of the correction lies within a given bound and adjusted so that successive model problems
approximate the true objective within the trust region. To solve trust region sub problem, both
the Cauchy point method and Dogleg method were used. Cauchy point performs poorly in some
cases. A significant improvement in convergence was achieved by using Dogleg method. Dogleg
method is more effective than Cauchy point and it reaches the convergence faster than Cauchy
point if it is started from the same initial point. The final algorithm was programmed in
MATLAB 8.1 and implemented on test problems and the result showed that the dogleg method
was far more superior in terms of speed and convergence than Cauchy method.
