Embodiments disclosed herein include methods for performing intensity-modulated radiation therapy on a subject using a plurality of pencil beams. The methods can include generating a treatment plan for intensity-modulated radiation therapy that satisfies dose constraints for each of a plurality of sub-volumes. The treatment plan can be generated using a superiorization technique that reduces total variation in dose space. Additional dose-volume constraints that permit a fraction of treatment doses to violate a prescription by up to a defined percentage of intensity can be used to assist in determining the treatment plan.