(679e) Variable Aggregation for Nonlinear Optimization

Large scale nonlinear programs (NLPs) are encountered frequently in chemical engineering applications. Successfully solving these nonlinear optimization problems online for various process parameters is key to achieving economic savings and continuous operation. However, state of the art non-linear solvers can face difficulties in convergence when optimizing for certain challenging applications. Variable aggregation has been studied in great detail as a pre-solve algorithm for linear and mixed integer optimization and has shown to help in solving challenging instances [1]. Although, more recently some nonlinear solvers and algebraic modeling languages have implemented variable aggregation as a pre-solve for nonlinear optimization problems, there exists no formal analysis on its impact on constrained nonlinear optimization problems.

We introduce a novel approximate maximum variable aggregation strategy [2] to aggregate as many variables as possible in an NLP. The approximate maximum variable aggregation is compared against other structure preserving variable aggregation approaches in terms of convergence reliability and solve time. Our results show that variable aggregation generally improves convergence reliability of the open-source nonlinear solver IPOPT [3]. Furthermore, variable aggregation can help in reducing the solve-time, however hessian evaluation can become a bottle neck if the number of nonlinear variables per constraint increases significantly due to aggregation.

In this talk, we describe our variable aggregation framework developed in Pyomo [4], give details on the approximate-maximum aggregation algorithm and demonstrate that variable aggregation can lead to better convergence reliability on various test problems.

References

[1] T. Achterberg, R. E. Bixby, Z. Gu, E. Rothberg, and D. Weninger, “Presolve Reductions in Mixed Integer Programming,” INFORMS Journal on Computing, Nov. 2019.

[2] S. Naik, L. Biegler, R. Bent, and R. Parker, “Variable aggregation for nonlinear optimization problems,” Feb. 21, 2025, arXiv: arXiv:2502.13869.

[3] A. Wächter, L. Biegler, Y. Lang, and A. Raghunathan, IPOPT: An interior point algorithm for large-scale nonlinear optimization. 2002.

[4] W. E. Hart, J.-P. Watson, and D. L. Woodruff, “Pyomo: modeling and solving mathematical programs in Python,” Mathematical Programming Computation, vol. 3, no. 3, pp. 219–260, 2011.