## Geometry of Semidefinite Max-Cut Relaxations via Ranks

Semidefinite programming (SDP) relaxations are proving to be a powerful tool for finding tight bounds for hard discrete optimization problems. This is especially true for one of the easier NP-hard problems, the Max-Cut problem (MC). The well-known SDP relaxation for Max-Cut, here denoted SDP1, can be derived by a first lifting into matrix space and … Read more

## Augmented self-concordant barriers and nonlinear optimization problems with finite complexity.

In this paper we study special barrier functions for the convex cones, which are the sum of a self-concordant barrier for the cone and a positive-semidefinite quadratic form. We show that the central path of these augmented barrier functions can be traced with linear speed. We also study the complexity of finding the analytic center … Read more

## Componentwise fast convergence in the solution of full-rank systems of nonlinear equations

The asymptotic convergence of parameterized variants of Newton’s method for the solution of nonlinear systems of equations is considered. The original system is perturbed by a term involving the variables and a scalar parameter which is driven to zero as the iteration proceeds. The exact local solutions to the perturbed systems then form a differentiable … Read more

## Sequence independent lifting for mixed-integer programming

We show that superadditive lifting functions lead to sequence independent lifting of inequalities for general mixed-integer programming. Citation Operations Research 52, 487-490, 2004

## An Interior-Point Perspective on Sensitivity Analysis in Semidefinite Programming

We study the asymptotic behavior of the interior-point bounds arising from the work of Yildirim and Todd on sensitivity analysis in semidefinite programming in comparison with the optimal partition bounds. For perturbations of the right-hand side vector and the cost matrix, we show that the interior-point bounds evaluated on the central path using the Monteiro-Zhang … Read more