Variable aggregation has been largely studied as an important pre-solve algorithm for optimization of linear and mixed-integer programs. Although some nonlinear solvers and algebraic modeling languages implement variable aggregation as a pre-solve, the impact it can have on constrained nonlinear programs is unexplored. In this work, we formalize variable aggregation as a pre-solve algorithm to develop reduced-space formulations of nonlinear programs. A novel approximate maximum variable aggregation strategy is developed to aggregate as many variables as possible. Furthermore, aggregation strategies that preserve the problem structure are compared against approximate maximum aggregation. Our results show that variable aggregation can generally help to improve the convergence reliability of nonlinear programs. It can also help in reducing total solve time. However, Hessian evaluation can become a bottleneck if aggregation significantly increases the number of variables appearing nonlinearly in many constraints.

翻译：变量聚合作为线性和混合整数规划优化的重要预求解算法已得到广泛研究。尽管部分非线性求解器及代数建模语言已实现变量聚合预求解功能，但其对约束非线性规划问题的影响尚未得到充分探索。本研究将变量聚合形式化为预求解算法，以构建非线性规划的降维空间表述。我们提出了一种新颖的近似最大变量聚合策略，旨在实现最大程度的变量聚合。此外，本文对比了保持问题结构的聚合策略与近似最大聚合策略的效果。研究结果表明，变量聚合通常能够提升非线性规划问题的收敛可靠性，并有助于减少总体求解时间。然而，若聚合过程显著增加在多个约束中非线性出现的变量数量，则Hessian矩阵求值可能成为计算瓶颈。