Methods For Unconstained Generalized Geometric Programming Problem

There are two basic approaches to solve nonlinear optimization problem namely: the line search method and the trust region method. Generalized geometric programming problem is a class of nonlinear optimization problem. Its objective function's Hession matrix has special construction.To make good use of this characteristics, we present two method to solve generalized geometric programming problem. Enlightened by the Gill-Murray method(cf. [23]), we present an improved Newton's algorithm and prove that the algorithm possesses convergence properties. Compared with line search method.trust region method has stronger convergence properties and robustness. However.it needs to resolve the subproblem repeatedly if the trial step results in an increase in the objective function. To overcome these shortcomings Nocedal and Yuan(cf. [24])propose the combining trust region method with line search technique.The second part of this thesis puts a method combining nonmonotone trust region technique with nonmonotone line search technique based on Armijo criterion to solve the problem and prove the convergence. Finally,numerical results are given to verify our algorithm.