10236 2026 eng B360 B385 3 48 article 0 2026-05-21 -- -- In practice, non-specialized interior-point algorithms often cannot utilize the massively parallel compute resources offered by modern many- and multi-core compute platforms. However, efficient distributed solution techniques are required, especially for large-scale linear programs. This article describes a new decomposition technique for systems of linear equations, implemented in the parallel interior-point solver PIPS-IPM++. The algorithm exploits a matrix structure commonly found in optimization problems: a doubly bordered block-diagonal or arrowhead structure with linking constraints and variables often only linking few, consecutive blocks. This structure is preserved in the linear KKT systems solved during each iteration of the interior-point method. We present a hierarchical Schur complement decomposition that distributes and solves the linear optimization problem. It is designed for high-performance architectures and scales well with the availability of additional computing resources. The decomposition approach uses the border constraints' locality to decouple the factorization process. Our approach is motivated by large-scale economic dispatch problems but can also be applied to other problem classes. We demonstrate the performance of our method on a set of mid- to large-scale instances, some of which have more than 10^9 nonzeros in their constraint matrices. SIAM Journal on Scientific Computing 2412.07731 10.1137/24M1716288 yes epub ahead of print publish urn:nbn:de:0297-zib-98829 Nils-Christian Kempke Janina Zittel Daniel Rehfeldt Thorsten Koch eng uncontrolled interior-point methods eng uncontrolled large-scale problems eng uncontrolled linear programming eng uncontrolled parallel computation eng uncontrolled mathematical programming eng uncontrolled direct methods for linear systems OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING Koch, Thorsten Rehfeldt, Daniel MODAL-Gesamt Applied Algorithmic Intelligence Methods MODAL-EnergyLab UNSEEN Kempke, Nils-Christian Applied Optimization