Steplengths in infeasible primal--dual interior point algorithms of convex quadratic programming

Csaba Meszaros

This paper concerns the infeasible primal-dual interior point methods for large-scale convex quadratic problems. Recent implementations of these algorithms use common steplengths in the primal and dual spaces during iterations which is achieved by ''damping'' the larger stepsize. In this paper a new approach is proposed to determine primal and dual stepsizes. The approach preserves the benefits of the steplength damping and reduces the primal and dual infeasibilities in each step. The advantage is that it allows different stepsizes in primal and dual and achieves better progress when approaching feasibility. The method is derived by investigating the efficient set of a multiobjective optimization problem. The usefulness of our proposed approach is demonstrated on a number of convex quadratic test problems.

Departmental Technical Report DOC 97/7, Imperial College, London, UK.