In this paper we follow up our discussion on algorithms suitable for optimization of systems governed by partial differential equations. In the first part of of this paper we proposed a Lagrange-Newton-Krylov-Schur method (LNKS) that uses Krylov iterations to solve the Karush-Kuhn-Tucker system of optimality conditions, but invokes a preconditioner inspired by reduced space quasi-Newton algorit...

We propose a path-following version of the Todd-Burrell procedure to solve linear programming problems with an unknown optimal value. The path-following scheme is not restricted to Karmarkar's primal step; it can also be implemented with a dual Newton step or with a primal-dual step.

Convergence properties are presented for Newton additive and multiplicative Schwarz iterative methods for the solution of nonlinear systems in several variables. These methods consist of approximate solutions of the linear Newton step using either additive or multiplicative Schwarz iterations, where overlap between subdomains can be used. Restricted versions of these methods are also considered...

The full-space Lagrange–Newton algorithm is one of the numerical algorithms for solving problems arising from optimization problems constrained by nonlinear partial differential equations. Newton-type methods enjoy fast convergence when the nonlinearity in the system is well-balanced; however, for some problems, such as the control of incompressible flows, even linear convergence is difficult t...

We describe the implementation details and give the experimental results of three optimization algorithms for dense optical flow computation. In particular, using a line search strategy, we evaluate the performance of the unilevel truncated Newton method (LSTN), a multiresolution truncated Newton (MR/LSTN) and a full multigrid truncated Newton (FMG/LSTN). We use three image sequences and four m...

The Hermitian and skew-Hermitian splitting (HSS) method is an unconditionally convergent iteration method for solving large sparse non-Hermitian positive definite system of linear equations. By making use of the HSS iteration as the inner solver for the Newton method, we establish a class of Newton-HSS methods for solving large sparse systems of nonlinear equations with positive definite Jacobi...

Contingency analysis plays an important role in assessing the static security of a network. Its purpose is to check whether system can operate safely when some elements are out service. In real-time application, computational time required perform calculation paramount for operators take immediate actions prevent cascading outages. Therefore, numerical performance contingency main focus this cu...