In part I of this article, we proposed a Lagrange–Newton–Krylov–Schur (LNKS) method for the solution of optimization problems that are constrained by partial differential equations. LNKS uses Krylov iterations to solve the linearized Karush–Kuhn–Tucker system of optimality conditions in the full space of states, adjoints, and decision variables, but invokes a preconditioner inspired by reduced ...

In this study we proposed two Quasi-Newton methods to deal with traffic assignment in the capacitated network. The methods combine Newton formula, column generation and penalty techniques. The first method employ the gradient of the objective function to obtain an improving feasible direction scaled by the second-order derivatives. The second one is to employ Rosen gradient to obtain an improvi...

Large-scale logistic regression arises in many applications such as document classification and natural language processing. In this paper, we apply a trust region Newton method to maximize the log-likelihood of the logistic regression model. The proposed method uses only approximate Newton steps in the beginning, but achieves fast convergence in the end. Experiments show that it is faster than...

A trust region-based optimization method has been incorporated into the DAKOTA optimization software toolkit. This trust region approach is designed to manage surrogate models of the objective and constraint functions during the optimization process. In this method, the surrogate functions are employed in a sequence of optimization steps, where the original expensive objective and constraint fu...

this study concerns with a trust-region-based method for solving unconstrained optimization problems. the approach takes the advantages of the compact limited memory bfgs updating formula together with an appropriate adaptive radius strategy. in our approach, the adaptive technique leads us to decrease the number of subproblems solving, while utilizing the structure of limited memory quasi-newt...