TRUST REGION METHOD FOR SOLVING UNCONSTRAINED NON LINEAR OPTIMIZATION PROBLEMS

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.