Direct Solution of Linear Systems of Size 109 Arising in Optimization with Interior Point Methods

摘要: Solution methods for very large scale optimization problems are addressed in this paper. Interior point demonstrated to provide unequalled efficiency context. They need a small (and predictable) number of iterations solve problem. A single iteration interior method requires the solution indefinite system equations. This is regularized guarantee existence triangular decomposition. Hence well-understood parallel computing techniques developed positive definite matrices can be extended class matrices. implementation an described It uses object-oriented programming and allows exploiting different block-structures Our outperforms industry-standard optimizer, shows good on massively architecture solves unprecedented sizes reaching 109 variables.