Interior-point methods possess strong theoretical properties and have been successfully applied to a wide variety of linear and nonlinear programming applications. This paper presents a class of algorithms, based on interior-point methodology, for performing regularized maximum likelihood reconstructions on 3-D emission tomography data. The algorithms solve a sequence of subproblems that conver...

It is well known that a large neighborhood interior point algorithm for linear optimization performs much better in implementation than its small neighborhood counterparts. One of the key elements of interior point algorithms is how to update the barrier parameter. The main goal of this paper is to introduce an “adaptive” long step interior-point algorithm in a large neighborhood of central pat...

It is well known that a wide-neighborhood interior-point algorithm for linear programming performs much better in implementation than small-neighborhood counterparts. In this paper, we provide a unified way to enlarge the neighborhoods of predictorcorrector interior-point algorithms for linear programming. We prove that our methods not only enlarge the neighborhoods but also retain the so-far b...

Interior Point Optimization techniques have recently emerged as a new tool for developing parameter estimation algorithms [1, 2]. These algorithms aim to take advantage of the fast convergence properties of interior point methods, to yield, in particular, fast transient performance. In this paper we develop a simple analytic center based algorithm, which updates estimates with a constant number...

  We present a new full Nesterov and Todd step infeasible interior-point algorithm for semi-definite optimization. The algorithm decreases the duality gap and the feasibility residuals at the same rate. In the algorithm, we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Every main iteration of the algorithm consists of a feasibili...

The literature on interior point algorithms shows impressive results related to the speed of convergence of the objective values, but very little is known about the convergence of the iterate sequences. This paper studies the horizontal linear complementarity problem, and derives general convergence properties for algorithms based on Newton iterations. This problem provides a simple and general...