Inability of low-resolution ocean models to simulate many important aspects of the large-scale general circulation is a common problem. In the view of physics, the main reason for this failure are the missed dynamical effects of the unresolved small scales of motion on the explicitly resolved large-scale circulation. Complimentary to this mainstream physics-based perspective, we propose to address this failure from the dynamical systems point of view, namely, as the persistent tendency of phase space trajectories representing the low-resolution solution to escape the right region of the corresponding phase space, which is occupied by the reference eddy-resolving solution. Based on this concept, we propose to use methods of constrained optimization to confine the low-resolution solution to remain within the correct phase space region, without attempting to amend the eddy physics by introducing a process-based parameterization. This approach is advocated as a novel framework for data-driven hyper-parameterizations of mesoscale oceanic eddies in non-eddy-resolving models. We tested the idea in the context of classical, baroclinic beta-plane turbulence model and showed that non-eddy-resolving solution can be substantially improved towards the reference eddy-resolving benchmark.