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This paper introduces SDSL-Solver, a distributed sparse linear solver framework tailored for interior point methods (IPMs) that addresses the computational bottleneck of solving sparse linear systems in large-scale optimization. SDSL-Solver leverages Krylov subspace methods with sparse filtering and diagonal correction to generate high-quality preconditioners, and offers both Block Jacobi and Bordered Block Diagonal (BBD) parallel methods to handle diverse problem characteristics. Experiments on problems with up to five million variables demonstrate significant speedups compared to PETSc and PARDISO, showcasing the scalability and efficiency of SDSL-Solver.
Solving massive optimization problems just got a whole lot faster: SDSL-Solver achieves up to 97x speedups over PARDISO by distributing sparse linear system solves across multiple nodes.
The solution of sparse linear systems constitutes the dominant computational bottleneck in interior point methods (IPMs), frequently consuming over 70\% of the total solution time. As optimization problems scale to millions of variables, direct solvers encounter prohibitive fill-in, excessive memory consumption, and limited parallel scalability. We present SDSL-Solver, a scalable distributed sparse linear solver framework designed for IPMs. SDSL-Solver employs Krylov subspace methods, combined with numerics-based sparse filtering and diagonal correction techniques that produce high-quality preconditioners. To accommodate diverse problem characteristics, SDSL-Solver offers two complementary distributed parallel methods: Block Jacobi for well-conditioned, diagonally dominant systems, and Bordered Block Diagonal (BBD) for ill-conditioned problems requiring globally coupled preconditioning via Schur complement techniques. A preconditioner reuse strategy further amortizes construction costs across consecutive IPMs iterations. We evaluate SDSL-Solver on benchmark problems with matrix dimensions ranging from tens of thousands to over five million on multi-node clusters equipped with X86 processors. The experimental results show that under the Block Jacobi and BBD distributed methods, SDSL-Solver on a four-node configuration achieves average speedups of $6.23\times$ and $7.77\times$, respectively, compared to PETSc running on the same number of nodes. Relative to the single-node PARDISO, the average speedups reach $97.54\times$ and $5.85\times$, respectively.
