Research on the Dual Problem of Trust Region Bundle Method

With the rapid development of science and technology as well as the cross-integration between the various disciplines, the nonsmooth optimization problem plays an increasingly important role in operational research. In this paper, we use the trust region method to study nonsmooth unconstrained optimization problems. Trust region subproblem is constructed to produce the next iteration point by using feasible set as constraint condition. As the number of iterations increases, the compression principle is used to control the elements in a bundle of information. And then the subproblem is studied by Lagrangian function and penalized bundle method [1]. The optimal solution and the relevant derivative conclusion are obtained by transforming the primal problem and dual problem into each other.