A trust-region framework for constrained optimization using reduced order modeling

Abstract

Reduced order models (ROM), such as proper orthogonal decomposition (POD), 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 around the point in decision variable space where they are constructed. Consequently, the ROM needs to be updated in a systematic manner over the course of the optimization. As an enabling strategy, trust-region methods provide an excellent adaptive framework for ROM-based optimization. They not only restrict the optimization step within the ROM’s validity, but also synchronize ROM updates with information obtained during the course of optimization, thus providing a robust and globally convergent framework. This study extends the trust-region framework to constrained optimization problems, using two approaches. We first develop an exact penalty-based trust-region algorithm with correction schemes to ensure global convergence with ROM-based approximate models. Next, we develop a novel filter trust-region algorithm which utilizes refinement of the ROM, and a feasibility restoration phase. Both algorithms are applied to the optimization of a two-bed four-step isothermal pressure swing adsorption (PSA) system, for CO2 capture. Although both algorithms converge to the same local optimum, the filter approach takes fewer trust-region iterations and requires less computational effort.