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...

All forms of the simplex method reach the optimum by traversing a series of basic solutions. Since each basic solution represents an extreme point of the feasible region, the track followed by the algorithm moves around the boundary of the feasible region. In the worst case, it may be necessary to examine most if not all of the extreme points. This can be cripplingly inefficient given that the ...

We investigate a preconditioning technique applied to the problem of solving linear systems arising from primal-dual interior point algorithms in linear and quadratic programming. The preconditioner has the attractive property of improved eigenvalue clustering with increased ill-conditioning of the (1, 1) block of the saddle point matrix. We demonstrate performance of the preconditioner on prob...

Carla T. L. S. Ghidini, Aurelio R. L. Oliveira, Jair Silva Institute of Mathematics, Statistics and Scientific of Computation (IMECC), State University of Campinas (UNICAMP), São Paulo, Brazil Federal University of Mato Grosso do Sul (UFMS), Mato Grosso do Sul, Brazil E-mail: {carla, aurelio}@ime.unicamp.br, [email protected] Received September 15, 2011; revised October 16, 2011; accepted Octobe...