On Generalized Primal-Dual Interior-Point Methods with Non-uniform Complementarity Perturbations for Quadratic Programming

This technical note discusses convergence conditions of a generalized variant of primal-dual interior point methods. The generalization arises due to the permitted case of having a non-uniform complementarity perturbation vector, which is equivalent to having different barrier parameters for each constraint instead of a global barrier parameter. Widely used prediction-correction methods and recently developed coordinated schemes can be considered as specific cases of the non-uniform perturbation framework. For convex quadratic programs, the polynomial complexity result of the standard feasible path following method with uniform perturbation vector is extended to the generalized case by imposing safeguarding conditions that keep the iterates close to the central-path.