A Novel Filter Trust-region Algorithm for Constrained Optimization Using Reduced Order Modeling

Reduced order models (ROM) lead to powerful techniques to address computational challenges in PDE-constrained optimization. However, when incorporated within optimization strategies, ROMs are sufficiently accurate only in a restricted zone and thus, need to be systematically updated over the course of the optimization. As an enabling strategy, trust-region methods provide an excellent adaptive framework for ROM-based optimization. This study develops a novel filter trust-region algorithm for constrained optimization problems, which utilizes ROM refinement and a feasibility restoration phase. The algorithm not only restricts the optimization step within ROM’s validity, but also synchronizes ROM updates with the information obtained during the course of optimization, thus providing a robust and globally convergent framework. When applied to the optimization of a two-bed four-step PSA system for CO2 capture, it converges to a local optimum within reasonable CPU time.