Trust Region Newton With Conjugate Gradient Method

In this project we give trust-region algorithms for nonlinear optimization. Trust-regionrnmethods are robust and can be applied to ill-conditioned problems. A conjugate gradientrntrust-region algorithm is presented to demonstrate the trust region approaches. Conver-rngence properties of trust-region with conjugate gradient are given. A trust-region methodrnsubproblems for solving unconstrained optimization is proposed. At every iteration, we usernthe conjugate gradient method or its variation to solve the subproblems approximately. Wernshow that this method has the same convergence properties as the trust-region method basedrnon the conjugate gradient method. Numerical results show that this method is as reliablernand more e cient in respect of iterations and evaluations using MATLAB.

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