We describe an interior point algorithm for convex quadratic problem with a strict complementarity constraints. We show that under some assumptions the approach requires a total of $O\left(\sqrt{n}L\right)$ number of iterations, where L is the input size of the problem. The algorithm generates a sequence of problems, each of which is approximately solved by Newton's method.

We propose a feasible primal-dual path-following interior-point algorithm for semidefinite least squares problems (SDLS). At each iteration, the algorithm uses only full Nesterov-Todd steps with the advantage that no line search is required. Under new appropriate choices of the parameter $\beta$ which defines the size of the neighborhood of the central-path and of the parameter $\theta$ which determines the rate of decrease of the barrier parameter, we show that the proposed algorithm is well defined and converges...

In this paper, we study the differentiability of the trajectories of the logarithmic barrier algorithm for a nonlinear program when the set Λ* of the Karush-Kuhn-Tucker multiplier vectors is empty owing to the fact that the constraint qualifications are not satisfied.