A new preconditioning approach for an interior point‐proximal method of multipliers for linear and convex quadratic programming

In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often large scale. With aim, devise an infeasible interior point method, blended with proximal method multipliers, which in turn results a primal-dual regularized method. Application gives rise to sequence increasingly ill-conditioned systems cannot always be solved by factorization methods, due memory CPU time restrictions. We propose novel preconditioning strategy is based on suitable sparsification normal equations matrix case, also constitutes foundation block-diagonal preconditioner accelerate MINRES for arising from general problems. Numerical range test problems demonstrate robustness proposed strategy, together its ability solve very dimension.