Parallel Inexact Newton and Interior Point Method
نویسنده
چکیده
In this paper we present the results obtained in the solution of sparse and large systems of non-linear equations by inexact Newton methods combined with an block iterative row-projection linear solver of Cimmino-type. Moreover, we propose a suitable partitioning of the Jacobian matrix A. In view of the sparsity, we obtain a mutually orthogonal row-partition of A that allows a simple solution of the linear least squares subproblems. We present numerical results obtained on a CRAY-T3E when this method is used to solve both non linear problems arising from dicretization of PDEs. Preliminary sequential results are also shown in the solution of nonlinear mixed complementary problems solved with interior point methods.
منابع مشابه
Global convergence of an inexact interior-point method for convex quadratic symmetric cone programming
In this paper, we propose a feasible interior-point method for convex quadratic programming over symmetric cones. The proposed algorithm relaxes the accuracy requirements in the solution of the Newton equation system, by using an inexact Newton direction. Furthermore, we obtain an acceptable level of error in the inexact algorithm on convex quadratic symmetric cone programmin...
متن کاملA nonmonotone inexact Newton method
In this paper we describe a variant of the Inexact Newton method for solving nonlinear systems of equations. We define a nonmonotone Inexact Newton step and a nonmonotone backtracking strategy. For this nonmonotone Inexact Newton scheme we present the convergence theorems. Finally, we show how we can apply these strategies to Inexact Newton Interior–Point method and we present some numerical ex...
متن کاملOn the Convergence of an Inexact Primal-Dual Interior Point Method for Linear Programming
The inexact primal-dual interior point method which is discussed in this paper chooses a new iterate along an approximation to the Newton direction. The method is the Kojima, Megiddo, and Mizuno globally convergent infeasible interior point algorithm The inexact variation is shown to have the same convergence properties accepting a residual in both the primal and dual Newton step equation also ...
متن کاملInterior Point Methods in Function Space for State Constraints - Inexact Newton and Adaptivity
We consider an interior point method in function space for PDE constrained optimal control problems with state constraints. Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error of each Newton step is c...
متن کاملInexact Newton Methods and Mixed Nonlinear Complementary Problems
In this paper we present the results obtained in the solution of sparse and large systems of nonlinear equations by Inexact Newton-like methods [6]. The linearized systems are solved with two preconditioners particularly suited for parallel computation. We report the results for the solution of some nonlinear problems on the CRAY T3E under the MPI environment. Our methods may be used to solve m...
متن کاملParallel Interior-Point Method for Linear and Quadratic Programs with Special Structure
This paper concerns the use of iterative solvers in interiorpoint methods for linear and quadratic programming problems. We state an adaptive termination rule for the inner iterative scheme and we prove the global convergence of the obtained algorithm, exploiting the theory developed for inexact Newton methods. This approach is promising for problems with special structure on parallel computers...
متن کامل