Radiotherapy is one of the most common forms of cancer treatment, given to nearly one million patients each year in the United States. It is a form of personalized medicine: everything from the orientation and modulation of the treatment beams to the treatment schedule, altogether, thousands of parameters, are tailored for each patient, using computational methods referred to as numerical optimization. Several recent technological, mathematical, and biological insights have motivated the departure from conventional forms of treatment; these include spatiotemporally fractionated therapy; proton therapy; combined photon, proton, and electron therapy; and arc therapy. However, the design of optimal personalized treatments with these new treatment approaches also present new mathematical challenges. This Faculty Early Career Development (CAREER) award funds research into the design and mathematical analysis of numerical optimization methods which, besides other applications in science and engineering, will enable the rigorous assessment and more widespread use of novel radiotherapy treatment modalities.
The focus of the project is the development and analysis of numerical methods for large-scale deterministic and stochastic optimization problems. The primary research objectives of this proposal are (1) to develop efficient sampling algorithms for large-scale stochastic constrained optimization, and (2) to develop numerical methods for large-scale convex conic optimization problems in which even a single Newton-step is too expensive. Both the mathematical and the applied components of the proposal are being integrated into the computational and modeling components of undergraduate and graduate courses developed by the PI. The grant also supports the PI's recently established outreach collaboration with artists and designers, which is aimed at broadening the public's appreciation and understanding of current applied mathematics research, in particular the importance of mathematical optimization in medicine, health care, and beyond.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
