A primal–dual interior-point algorithm for quadratic programming

In this paper we propose a primal–dual interior-point method for large, sparse, quadratic programming problems. The method is based on a reduction presented by Gonzalez-Lima, Wei, and Wolkowicz in order to solve the linear systems arising in the primal–dual methods for linear programming. The main features of this reduction are that it is well defined at the solution set and it preserves sparsity. These properties add robustness and stability to the algorithm and very accurate solutions can be obtained. We describe the method and we consider different reductions using the same framework. We discuss the relationship of our proposals and the one used in the LOQO code. We compare and study the different approaches by performing numerical experimentation using problems from the Maros and Meszaros collection. We also include a brief discussion on the meaning and effect of ill-conditioning when solving linear systems.