This talk will be based on a paper by Dominguez and Gonzalez-Lima where a primal-dual interior-point method for (large, sparse) quadratic programming problems is proposed. The method relies 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 is 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.
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