It was brought to our attention by Professor Valeria Simoncini that our proof of Theorem 2.1 [2, p. 139] is incorrect. Indeed, on page 140 we write the inequality (2.4) which is correct because we work with à which is an m× n matrix and m ≤ n and rank(A)=m hence ‖ÃT y‖ ‖y‖ ≥ σ̃1. However, on page 141 we write the inequality (2.6). We try to use a similar argument but now instead of à we have à a...

We describe an implementation of an infinite-dimensional primal-dual algorithm based on the Nesterov-Todd direction. Several applications to both continuous and discrete-time multi-criteria linear-quadratic control problems and linear-quadratic control problem with quadratic constraints are described. Numerical results show a very fast convergence (typically, within 3-4 iterations) to optimal s...

We address the iterative solution of KKT systems arising in the solution of convex quadratic programming problems. Two strictly related and well established formulations for such systems are studied with particular emphasis on the effect of preconditioning strategies on their relation. Constraint and augmented preconditioners are considered, and the choice of the augmentation matrix is discusse...

We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with an apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to generate such solutions. The method of proof is based on the barrier method used by Isenberg for compact manifolds without boundary, suitably extended to accommodat...

This paper characterizes completely the behavior of the logarithmic barrier method under a standard second order condition, strict (multivalued) complementarity and MFCQ at a local minimizer. We present direct proofs, based on certain key estimates and few well-known facts on linear and parametric programming, in order to verify existence and Lipschitzian convergence of local primal-dual soluti...

We discuss fast implementations of primal-dual interior-point methods for semidefinite programs derived from the Kalman-Yakubovich-Popov lemma, a class of problems that are widely encountered in control and signal processing applications. By exploiting problem structure we achieve a reduction of the complexity by several orders of magnitude compared to generalpurpose semidefinite programming so...

We study the extreme singular values of incidence graph matrices, obtaining lower and upper estimates that are asymptotically tight. This analysis is then used for obtaining estimates on the spectral condition number of some weighted graph matrices. A short discussion on possible preconditioning strategies within interior-point methods for network flow problems is also included.

We study monotonicity of primal and dual objective values in the framework of primal-dual interior-point methods. The primal-dual aane-scaling algorithm is monotone in both objectives. We derive a condition under which a primal-dualinterior-point algorithm with a centering component is monotone. Then we propose primal-dual algorithms that are monotone in both primal and dual objective values an...

We analyze a primal-dual interior-point method for nonlinear programming. We prove the global convergence for a wide class of problems under the standard assumptions on the problem.

We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to generate such solutions. The method of proof is based on the barrier method introduced by Isenberg for compact manifolds without boundary,suitably extended to accommod...