Optimization using the L∞ norm is an increasingly important area in multiview geometry. Previous work has shown that globally optimal solutions can be computed reliably using the formulation of generalized fractional programming, in which algorithms solve a sequence of convex problems independently to approximate the optimal L∞ norm error. We found the sequence of convex problems are highly rel...

This paper proposes a new primal-dual predictor-corrector interior-point method for a class of semideenite programs, which numerically traces the central trajectory in a space of Lagrange multipliers. The distinguishing features of the method are full use of the BFGS quasi-Newton method in the corrector procedure and an application of the conjugate gradient method with an eeective preconditioni...

We give a framework for the globalization of a nonsmooth Newton method. In part one we start with recalling B. Kummer's approach to convergence analysis of a nonsmooth Newton method and state his results for local convergence. In part two we give a globalized version of this method. Our approach uses a path search idea to control the descent. After elaborating the single steps, we analyze and p...

A general outer iteration, based upon linearization, is introduced at discrete time steps for the one-dimensional semiconductor device model. The iteration depends upon solving the semidiscrete device equations approximately, specifically, in such a way that the residual is of order ∆t in an appropriate norm. It is shown that this maintains the order of the backward Euler method. A monitoring o...

Most existing methods for calculating the steady state solution of the lattice Boltzmann equations are based on pseudo time stepping, which often requires a large number of time steps especially for high Reynolds number problems. To calculate the steady state solution directly without the time integration, in this paper we propose and study a nonlinearly preconditioned inexact Newton algorithm ...

Current successful methods for solving semidefinite programs, SDP, are based on primal-dual interior-point approaches. These usually involve a symmetrization step to allow for application of Newton’s method followed by block elimination to reduce the size of the Newton equation. Both these steps create ill-conditioning in the Newton equation and singularity of the Jacobian of the optimality con...

We investigate a semi-smooth Newton method for the numerical solution of optimal control problems subject to differential-algebraic equations (DAEs) and mixed control-state constraints. The necessary conditions are stated in terms of a local minimum principle. By use of the Fischer-Burmeister function the local minimum principle is transformed into an equivalent nonlinear and semi-smooth equati...

A Newton–Krylov method is an implementation of Newton’s method in which a Krylov subspace method is used to solve approximately the linear systems that characterize steps of Newton’s method. Newton–Krylov methods are often implemented in “matrix-free” form, in which the Jacobian-vector products required by the Krylov solver are approximated by finite differences. Here we consider using approxim...

Null space Newton algorithms are efficient in solving the nonlinear equations arising in hydraulic analysis of water distribution networks. In this article, we propose and evaluate an inexact Newton method that relies on partial updates of the network pipes’ frictional headloss computations to solve the linear systems more efficiently and with numerical reliability. The update set parameters ar...