In this paper, a novel decoding algorithm for lowdensity parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector channels include many practically important channels such as inter symbol interference channels and partial response channels. It is shown that the maximum l...

In applied sciences PDEs model an extensive variety of phenomena. Typically the final goal of simulations is a system which is optimal in a certain sense. For instance optimal control problems identify a control to steer a system towards a desired state. Inverse problems seek PDE parameters which are most consistent with measurements. In these optimization problems PDEs appear as equality const...

We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semideenite matrices. We show that the approach is very eecient for graph bisection problems, such as max-cut. Other applications include max-min eigenvalue problems and relaxations for the stable set problem.

A primal-dual interior point method for optimal control problems is considered. The algorithm is directly applied to the infinite-dimensional problem. Existence and convergence of the central path are analyzed, and linear convergence of a short-step path-following method is established.

This paper presents an alternating minimization (AM) algorithm used in the training of radial basis function and linear regressor networks. The algorithm is a modification of a small-step interior point method used in solving primal linear programs. The algorithm has a convergence rate of O( fo,L) iterations where n is a measure of the network size and L is a measure of the resulting solution's...

The main cost of solving a linear programming problem using an interior point method is usually the cost of solving a series of sparse, symmetric linear systems of equations, AA T x = b. These systems are typically solved using a sparse direct method. The rst step in such a method is a reordering of the rows and columns of the matrix to reduce ll in the factor and/or reduce the required work. T...

In this paper, we propose a primal IP method for solving the optimal experimental design problem with a large class of smooth convex optimality criteria, including A-, Dand pth mean criterion, and establish its global convergence. We also show that the Newton direction can be computed efficiently when the size of the moment matrix is small relative to the sample size. We compare our IP method w...

In this report a thematic, formal model for classification of the interior of buildings is created. Firstly, a description of how objects can be reconstructed from laser scanning point clouds is given. Secondly, the thematic, formal model is described. Thirdly, how to store this model in a database is described. At the moment, the need for an accurate description of the interior of buildings (‘...

Many issues that are crucial for an e cient implementation of an interior point algorithm are addressed in this chapter. To start with, a prototype primaldual algorithm is presented. Next, many tricks that make it e cient in practice are discussed in detail. Those include: preprocessing techniques, initialization approaches, methods for computing search directions (and the underlying linear alg...