We focus on the numerical solution of medium scale bound-constrained systems of nonlinear equations. In this context, we consider an affinescaling trust region approach that allows a great flexibility in choosing the scaling matrix used to handle the bounds. The method is based on a dogleg procedure tailored for constrained problems and so, it is named Constrained Dogleg method. It generates on...

Within the framework of affine scaling trust-region methods for bound constrained problems, we discuss the use of a inexact dogleg method as a tool for simultaneously handling the trust-region and the bound constraints while seeking for an approximate minimizer of the model. Focusing on bound-constrained systems of nonlinear equations, an inexact affine scaling method for large scale problems, ...

The diierential dynamic programming algorithm (DDP) and the stage-wise Newton procedure are two typical examples of eecient local procedures for discrete-time optimal control (DTOC) problems. It is desirable to generalize these local procedures to globally convergent methods. One successful globalization was recently proposed by Coleman and Liao 3] which combines the trust region idea with Pant...

In this article, we present an algorithm which is capable of transforming a gridded dogleg channel routing problem into a constraint programming (CP) problem. The transformed CP problem consists of a set of variables and a list of constraints; it can be solved by JaCoP, a finite-domain constraint programming solver. For a given dogleg channel routing problem, our approach is able to minimize th...

Channel routing is a key problem in the physical design of VLSI chips. It is known that ma4dmz, urn,,) is a lower bound on the number of tmcka requared in the reserved two-layer Manhattan routine model. where d,,,,, is the channel density and vi, is the length oftKe longest path in the vertical constraint omvh. In this paver we vropose a polynomial time algorithm that ‘wmput’es a better and non...

Two dipole doglegs are widely used to translate the beam axis horizontally or vertically. Quadrupoles are placed between the two consecutive dipoles to match first order dispersion and provide betatron focusing. Similarly a four dipole chicane is usually employed to form a bypass region, where the beam axis is transversely shifted first, then translated back to the original axis. In order to ge...

The velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared residuals. A finite element discretization of the functional is minimized by a trust-region method in which the trust-region radius is defined by a Sobolev norm and the trust-reg...

We show that channel routing in the Manhattan model remains diicult even when all nets are single-sided. Given a set of n single-sided nets, we consider the problem of determining the minimum number of tracks required to obtain a dogleg-free routing. In addition to showing that the decision version of the problem is NP-complete, we show that there are problems requiring at least d + (p n) track...

The present article concentrates on the dogleg-free Manhattan model where horizontal and vertical wire segments are positioned on different sides of the board and each net (wire) has at most one horizontal segment. While the minimum width can be found in linear time in the single row routing, apparently there was no efficient algorithm to find the minimum wire length. We show that there is no h...