The use of mathematical optimization to design cancer treatment plans, called inverse planning, has been an active field of research---and even practice---in radiation treatment planning, including intensity modulated radiation therapy, stereotactic radiosurgery, proton therapy, and brachytherapy. The mathematical differences between radiation dose deposition and thermal damage (additive radiation dose versus thermal dose described by partial differential equations) mean that radiation-based optimization models are not directly applicable to high intensity ultrasound (HIFU) treatments, however, the basic framework provides a template that can be used for HIFU optimization. In particular, recent advances in inverse planning optimization for focal ablation treatments share many of the same computational and clinical properties as HIFU, and can be used as a proof of concept for HIFU optimization. This talk will cover the principles behind inverse planning optimization for both radiation and thermal dose (ablation and HIFU) based treatments, and discuss knowledge gaps that must be closed before HIFU optimization is clinically viable from an optimization perspective.