A new method for projection based model reduction of linear inequality constrained systems

Computational modeling research centers around developing ever better representations of physics. The objective of model reduction specialists is to take that high fidelity understanding and compress it into a Reduced Order Model (ROM) capable of replicating the physical accuracy of the more complicated model with a significantly reduced computational cost. A current challenge in reduced order modeling is the presence of linear inequality constraints in optimization problems. Constrained optimization problems arise in design, contact modeling, financial engineering and other subfields of mathematical modeling. As such, there is a strong motivation to leverage the repeatability of ROMs to rapidly address these engineering challenges. Inherent to the problem of con- strained optimization is feasibility of solutions, and while all FOMs are expected to comply perfectly with their constraints, that property is not necessarily preserved in their corresponding ROMs. The problem is then two fold. First the issue of the constraint must be addressed, and second the resulting ROM must obey the constraints. This thesis develops a method, in a projection-based framework, capable of reducing the linear inequality constraints while preserving a strong degree of feasibility. The proposed method is successfully applied to the reduction of the one-dimensional, constrained Poisson Equation with varied parameters