  We present a component-based model order reduction procedure to efficiently
and accurately solve parameterized incompressible flows governed by the
Navier-Stokes equations. Our approach leverages a non-overlapping
optimization-based domain decomposition technique to determine the control
variable that minimizes jumps across the interfaces between sub-domains. To
solve the resulting constrained optimization problem, we propose both
Gauss-Newton and sequential quadratic programming methods, which effectively
transform the constrained problem into an unconstrained formulation.
Furthermore, we integrate model order reduction techniques into the
optimization framework, to speed up computations. In particular, we incorporate
localized training and adaptive enrichment to reduce the burden associated with
the training of the local reduced-order models. Numerical results are presented
to demonstrate the validity and effectiveness of the overall methodology.
