Active Noise Cancellation (ANC) at a target area in an open space, as opposed to cancellation in the ears through headphones, can lead to future applications. For instance, a personal acoustic environment in an airplane seat or inside a car, or a quiet zone in a noisy shared workspace can be possible using such open-space ANC without any uncomfortable on-body audio equipment. Recent advancements reinforce the practicality of such systems. However, regularization of the cancellation signal has been a crucial challenge in open-space ANC as it causes amplification of noise at locations away from the target area. This work presents a spherical harmonics-domain feed-forward spatial ANC method with a room-wide global cost function to address this issue. This room-wide global cost function is used for optimizing the set of regularization hyperparameters, while at run time only local information captured by a microphone array surrounding the target listening zone is required. Numerical experiments applying the proposed method in a simulated reverberant room show the effectiveness of the proposed method in creating a specific zone of silence with low to moderate noise amplification in the rest of the room.