An interior-point method for efficient solution of block-structured NLP problems using an implicit Schur-complement decomposition

作者：Kang Jia; Cao Yankai; Word Daniel P; Laird C D^*

来源：Computers & Chemical Engineering, 2014, 71: 563-573.

DOI：10.1016/j.compchemeng.2014.09.013

• Parallel computing
• Interior-point
• Nonlinear programming
• Schur complement decomposition

In this work, we address optimization of large-scale, nonlinear, block-structured problems with a significant number of coupling variables. Solving these problems using interior-point methods requires the solution of a linear system that has a block-angular structure at each iteration. Parallel solution is possible using a Schur-complement decomposition. In an explicit Schur-complement decomposition, the computational cost of forming and factorizing the Schur-complement is prohibitive for problems with many coupling variables. In this paper, we show that this bottleneck can be overcome by solving the Schur-complement equations implicitly, using a quasi-Newton preconditioned conjugate gradient method. This new algorithm avoids explicit formation and factorization of the Schur-complement. The computational efficiency of this algorithm is compared with the serial full-space approach, and the serial and parallel explicit Schur-complement approach. These results show that the PCG Schur-complement approach dramatically reduces the computational cost for problems with many coupling variables.

• 出版日期2014-12-4