A new method of moving asymptotes for large-scale unconstrained optimization

The method of moving asymptotes is known to work well in the context of structural optimization. A new method of moving asymptotes is proposed for solving large-scale unconstrained optimization problems in this paper. In this method, a descending direction is obtained by solving a convex separable subproblem of moving asymptotes in each iteration. New rules for controlling the asymptotes parameters are designed by using the trust region radius and some approximation properties such that the global convergence of this method is obtained. In addition, a linear search technique is inserted in case of the failure of trust region steps. The numerical results show that the new method may be capable of processing some large-scale problems.